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+{"instance_id":"countdown_2k_0","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 48, 35, 6]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [44, 48, 35, 6], target: 25. Options for choosing two numbers: [(44, 48), (44, 35), (44, 6), (48, 35), (48, 6), (35, 6)].\n |- Pick two numbers (44, 48) (numbers left: [35, 6]). Try possible operations.\n  |- Try 48 + 44 = 92. Add 92 to the number set. Current number set: [92, 35, 6], target: 25. Options for choosing two numbers: [(92, 35), (92, 6), (35, 6)].\n   |- Pick two numbers (92, 35) (numbers left: [6]). Try possible operations.\n    |- Try 92 + 35 = 127. Add 127 to the number set. Current number set: [127, 6], target: 25, just two numbers left.\n     |- Try 127 + 6 = 133. Evaluate 133 != 25, drop this branch.\n     |- Try 127 - 6 = 121. Evaluate 121 != 25, drop this branch.\n     |- Try 127 * 6 = 762. Evaluate 762 != 25, drop this branch.\n     |- Try 127 \/ 6 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 92 - 35 = 57. Add 57 to the number set. Current number set: [57, 6], target: 25, just two numbers left.\n     |- Try 57 + 6 = 63. Evaluate 63 != 25, drop this branch.\n     |- Try 57 - 6 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 57 * 6 = 342. Evaluate 342 != 25, drop this branch.\n     |- Try 57 \/ 6 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 92 * 35 = 3220. 3220 exceeds the maximum intermediate result, drop this branch.\n    |- Try 92 \/ 35 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (92, 6) (numbers left: [35]). Try possible operations.\n    |- Try 92 + 6 = 98. Add 98 to the number set. Current number set: [98, 35], target: 25, just two numbers left.\n     |- Try 98 + 35 = 133. Evaluate 133 != 25, drop this branch.\n     |- Try 98 - 35 = 63. Evaluate 63 != 25, drop this branch.\n     |- Try 98 * 35 = 3430. 3430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 35 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 92 - 6 = 86. Add 86 to the number set. Current number set: [86, 35], target: 25, just two numbers left.\n     |- Try 86 + 35 = 121. Evaluate 121 != 25, drop this branch.\n     |- Try 86 - 35 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 86 * 35 = 3010. 3010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 35 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 92 * 6 = 552. Add 552 to the number set. Current number set: [552, 35], target: 25, just two numbers left.\n     |- Try 552 + 35 = 587. Evaluate 587 != 25, drop this branch.\n     |- Try 552 - 35 = 517. Evaluate 517 != 25, drop this branch.\n     |- Try 552 * 35 = 19320. 19320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 552 \/ 35 = 15.8. 15.8 is a decimal, drop this branch.\n    |- Try 92 \/ 6 = 15.3. 15.3 is a decimal, drop this branch.\n   |- Pick two numbers (35, 6) (numbers left: [92]). Try possible operations.\n    |- Try 35 + 6 = 41. Add 41 to the number set. Current number set: [41, 92], target: 25, just two numbers left.\n     |- Try 92 + 41 = 133. Evaluate 133 != 25, drop this branch.\n     |- Try 92 - 41 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 92 * 41 = 3772. 3772 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 41 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 35 - 6 = 29. Add 29 to the number set. Current number set: [29, 92], target: 25, just two numbers left.\n     |- Try 92 + 29 = 121. Evaluate 121 != 25, drop this branch.\n     |- Try 92 - 29 = 63. Evaluate 63 != 25, drop this branch.\n     |- Try 92 * 29 = 2668. 2668 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 29 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 35 * 6 = 210. Add 210 to the number set. Current number set: [210, 92], target: 25, just two numbers left.\n     |- Try 210 + 92 = 302. Evaluate 302 != 25, drop this branch.\n     |- Try 210 - 92 = 118. Evaluate 118 != 25, drop this branch.\n     |- Try 210 * 92 = 19320. 19320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 92 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 35 \/ 6 = 5.8. 5.8 is a decimal, drop this branch.\n  |- Try 48 - 44 = 4. Add 4 to the number set. Current number set: [4, 35, 6], target: 25. Options for choosing two numbers: [(4, 35), (4, 6), (35, 6)].\n   |- Pick two numbers (4, 35) (numbers left: [6]). Try possible operations.\n    |- Try 35 + 4 = 39. Add 39 to the number set. Current number set: [39, 6], target: 25, just two numbers left.\n     |- Try 39 + 6 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 39 - 6 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 39 * 6 = 234. Evaluate 234 != 25, drop this branch.\n     |- Try 39 \/ 6 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 35 - 4 = 31. Add 31 to the number set. Current number set: [31, 6], target: 25, just two numbers left.\n     |- Try 31 + 6 = 37. Evaluate 37 != 25, drop this branch.\n     |- Try 31 - 6 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 - 6 = 25\nThe step before: 35 - 4 = 31\nThe first step: 48 - 44 = 4\n\nOutput the solution in the required format:\n<Solution>\n48 - 44 = 4\n35 - 4 = 31\n31 - 6 = 25\n<\/Solution>\n","item":{"nums":[44,48,35,6],"solution":["48 - 44 = 4","35 - 4 = 31","31 - 6 = 25"],"target":25}}
+{"instance_id":"countdown_2k_1","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 33, 39, 2]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [15, 33, 39, 2], target: 23. Options for choosing two numbers: [(15, 33), (15, 39), (15, 2), (33, 39), (33, 2), (39, 2)].\n |- Pick two numbers (15, 33) (numbers left: [39, 2]). Try possible operations.\n  |- Try 33 + 15 = 48. Add 48 to the number set. Current number set: [48, 39, 2], target: 23. Options for choosing two numbers: [(48, 39), (48, 2), (39, 2)].\n   |- Pick two numbers (48, 39) (numbers left: [2]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 2], target: 23, just two numbers left.\n     |- Try 87 + 2 = 89. Evaluate 89 != 23, drop this branch.\n     |- Try 87 - 2 = 85. Evaluate 85 != 23, drop this branch.\n     |- Try 87 * 2 = 174. Evaluate 174 != 23, drop this branch.\n     |- Try 87 \/ 2 = 43.5. 43.5 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 2], target: 23, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 23, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 23, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 23, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 2], target: 23, just two numbers left.\n     |- Try 1872 + 2 = 1874. Evaluate 1874 != 23, drop this branch.\n     |- Try 1872 - 2 = 1870. Evaluate 1870 != 23, drop this branch.\n     |- Try 1872 * 2 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 2 = 936. Evaluate 936 != 23, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (48, 2) (numbers left: [39]). Try possible operations.\n    |- Try 48 + 2 = 50. Add 50 to the number set. Current number set: [50, 39], target: 23, just two numbers left.\n     |- Try 50 + 39 = 89. Evaluate 89 != 23, drop this branch.\n     |- Try 50 - 39 = 11. Evaluate 11 != 23, drop this branch.\n     |- Try 50 * 39 = 1950. Evaluate 1950 != 23, drop this branch.\n     |- Try 50 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 - 2 = 46. Add 46 to the number set. Current number set: [46, 39], target: 23, just two numbers left.\n     |- Try 46 + 39 = 85. Evaluate 85 != 23, drop this branch.\n     |- Try 46 - 39 = 7. Evaluate 7 != 23, drop this branch.\n     |- Try 46 * 39 = 1794. Evaluate 1794 != 23, drop this branch.\n     |- Try 46 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 2 = 96. Add 96 to the number set. Current number set: [96, 39], target: 23, just two numbers left.\n     |- Try 96 + 39 = 135. Evaluate 135 != 23, drop this branch.\n     |- Try 96 - 39 = 57. Evaluate 57 != 23, drop this branch.\n     |- Try 96 * 39 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 39 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 \/ 2 = 24. Add 24 to the number set. Current number set: [24, 39], target: 23, just two numbers left.\n     |- Try 39 + 24 = 63. Evaluate 63 != 23, drop this branch.\n     |- Try 39 - 24 = 15. Evaluate 15 != 23, drop this branch.\n     |- Try 39 * 24 = 936. Evaluate 936 != 23, drop this branch.\n     |- Try 39 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (39, 2) (numbers left: [48]). Try possible operations.\n    |- Try 39 + 2 = 41. Add 41 to the number set. Current number set: [41, 48], target: 23, just two numbers left.\n     |- Try 48 + 41 = 89. Evaluate 89 != 23, drop this branch.\n     |- Try 48 - 41 = 7. Evaluate 7 != 23, drop this branch.\n     |- Try 48 * 41 = 1968. Evaluate 1968 != 23, drop this branch.\n     |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 2 = 37. Add 37 to the number set. Current number set: [37, 48], target: 23, just two numbers left.\n     |- Try 48 + 37 = 85. Evaluate 85 != 23, drop this branch.\n     |- Try 48 - 37 = 11. Evaluate 11 != 23, drop this branch.\n     |- Try 48 * 37 = 1776. Evaluate 1776 != 23, drop this branch.\n     |- Try 48 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 39 * 2 = 78. Add 78 to the number set. Current number set: [78, 48], target: 23, just two numbers left.\n     |- Try 78 + 48 = 126. Evaluate 126 != 23, drop this branch.\n     |- Try 78 - 48 = 30. Evaluate 30 != 23, drop this branch.\n     |- Try 78 * 48 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 48 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n  |- Try 33 - 15 = 18. Add 18 to the number set. Current number set: [18, 39, 2], target: 23. Options for choosing two numbers: [(18, 39), (18, 2), (39, 2)].\n   |- Pick two numbers (18, 39) (numbers left: [2]). Try possible operations.\n    |- Try 39 + 18 = 57. Add 57 to the number set. Current number set: [57, 2], target: 23, just two numbers left.\n     |- Try 57 + 2 = 59. Evaluate 59 != 23, drop this branch.\n     |- Try 57 - 2 = 55. Evaluate 55 != 23, drop this branch.\n     |- Try 57 * 2 = 114. Evaluate 114 != 23, drop this branch.\n     |- Try 57 \/ 2 = 28.5. 28.5 is a decimal, drop this branch.\n    |- Try 39 - 18 = 21. Add 21 to the number set. Current number set: [21, 2], target: 23, just two numbers left.\n     |- Try 21 + 2 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 + 2 = 23\nThe step before: 39 - 18 = 21\nThe first step: 33 - 15 = 18\n\nOutput the solution in the required format:\n<Solution>\n33 - 15 = 18\n39 - 18 = 21\n21 + 2 = 23\n<\/Solution>\n","item":{"nums":[15,33,39,2],"solution":["33 - 15 = 18","39 - 18 = 21","21 + 2 = 23"],"target":23}}
+{"instance_id":"countdown_2k_2","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 6, 49, 4]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [32, 6, 49, 4], target: 27. Options for choosing two numbers: [(32, 6), (32, 49), (32, 4), (6, 49), (6, 4), (49, 4)].\n |- Pick two numbers (32, 6) (numbers left: [49, 4]). Try possible operations.\n  |- Try 32 + 6 = 38. Add 38 to the number set. Current number set: [38, 49, 4], target: 27. Options for choosing two numbers: [(38, 49), (38, 4), (49, 4)].\n   |- Pick two numbers (38, 49) (numbers left: [4]). Try possible operations.\n    |- Try 49 + 38 = 87. Add 87 to the number set. Current number set: [87, 4], target: 27, just two numbers left.\n     |- Try 87 + 4 = 91. Evaluate 91 != 27, drop this branch.\n     |- Try 87 - 4 = 83. Evaluate 83 != 27, drop this branch.\n     |- Try 87 * 4 = 348. Evaluate 348 != 27, drop this branch.\n     |- Try 87 \/ 4 = 21.8. 21.8 is a decimal, drop this branch.\n    |- Try 49 - 38 = 11. Add 11 to the number set. Current number set: [11, 4], target: 27, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 != 27, drop this branch.\n     |- Try 11 \/ 4 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 49 * 38 = 1862. Add 1862 to the number set. Current number set: [1862, 4], target: 27, just two numbers left.\n     |- Try 1862 + 4 = 1866. Evaluate 1866 != 27, drop this branch.\n     |- Try 1862 - 4 = 1858. Evaluate 1858 != 27, drop this branch.\n     |- Try 1862 * 4 = 7448. 7448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1862 \/ 4 = 465.5. 465.5 is a decimal, drop this branch.\n    |- Try 49 \/ 38 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (38, 4) (numbers left: [49]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 49], target: 27, just two numbers left.\n     |- Try 49 + 42 = 91. Evaluate 91 != 27, drop this branch.\n     |- Try 49 - 42 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 49 * 42 = 2058. 2058 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 49], target: 27, just two numbers left.\n     |- Try 49 + 34 = 83. Evaluate 83 != 27, drop this branch.\n     |- Try 49 - 34 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 49 * 34 = 1666. Evaluate 1666 != 27, drop this branch.\n     |- Try 49 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 49], target: 27, just two numbers left.\n     |- Try 152 + 49 = 201. Evaluate 201 != 27, drop this branch.\n     |- Try 152 - 49 = 103. Evaluate 103 != 27, drop this branch.\n     |- Try 152 * 49 = 7448. 7448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 152 \/ 49 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (49, 4) (numbers left: [38]). Try possible operations.\n    |- Try 49 + 4 = 53. Add 53 to the number set. Current number set: [53, 38], target: 27, just two numbers left.\n     |- Try 53 + 38 = 91. Evaluate 91 != 27, drop this branch.\n     |- Try 53 - 38 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 53 * 38 = 2014. 2014 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 38 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 49 - 4 = 45. Add 45 to the number set. Current number set: [45, 38], target: 27, just two numbers left.\n     |- Try 45 + 38 = 83. Evaluate 83 != 27, drop this branch.\n     |- Try 45 - 38 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 45 * 38 = 1710. Evaluate 1710 != 27, drop this branch.\n     |- Try 45 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 * 4 = 196. Add 196 to the number set. Current number set: [196, 38], target: 27, just two numbers left.\n     |- Try 196 + 38 = 234. Evaluate 234 != 27, drop this branch.\n     |- Try 196 - 38 = 158. Evaluate 158 != 27, drop this branch.\n     |- Try 196 * 38 = 7448. 7448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 38 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n  |- Try 32 - 6 = 26. Add 26 to the number set. Current number set: [26, 49, 4], target: 27. Options for choosing two numbers: [(26, 49), (26, 4), (49, 4)].\n   |- Pick two numbers (26, 49) (numbers left: [4]). Try possible operations.\n    |- Try 49 + 26 = 75. Add 75 to the number set. Current number set: [75, 4], target: 27, just two numbers left.\n     |- Try 75 + 4 = 79. Evaluate 79 != 27, drop this branch.\n     |- Try 75 - 4 = 71. Evaluate 71 != 27, drop this branch.\n     |- Try 75 * 4 = 300. Evaluate 300 != 27, drop this branch.\n     |- Try 75 \/ 4 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 49 - 26 = 23. Add 23 to the number set. Current number set: [23, 4], target: 27, just two numbers left.\n     |- Try 23 + 4 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 4 = 27\nThe step before: 49 - 26 = 23\nThe first step: 32 - 6 = 26\n\nOutput the solution in the required format:\n<Solution>\n32 - 6 = 26\n49 - 26 = 23\n23 + 4 = 27\n<\/Solution>\n","item":{"nums":[32,6,49,4],"solution":["32 - 6 = 26","49 - 26 = 23","23 + 4 = 27"],"target":27}}
+{"instance_id":"countdown_2k_3","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [21, 32, 2, 8]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [21, 32, 2, 8], target: 17. Options for choosing two numbers: [(21, 32), (21, 2), (21, 8), (32, 2), (32, 8), (2, 8)].\n |- Pick two numbers (21, 32) (numbers left: [2, 8]). Try possible operations.\n  |- Try 32 + 21 = 53. Add 53 to the number set. Current number set: [53, 2, 8], target: 17. Options for choosing two numbers: [(53, 2), (53, 8), (2, 8)].\n   |- Pick two numbers (53, 2) (numbers left: [8]). Try possible operations.\n    |- Try 53 + 2 = 55. Add 55 to the number set. Current number set: [55, 8], target: 17, just two numbers left.\n     |- Try 55 + 8 = 63. Evaluate 63 != 17, drop this branch.\n     |- Try 55 - 8 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 55 * 8 = 440. Evaluate 440 != 17, drop this branch.\n     |- Try 55 \/ 8 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 53 - 2 = 51. Add 51 to the number set. Current number set: [51, 8], target: 17, just two numbers left.\n     |- Try 51 + 8 = 59. Evaluate 59 != 17, drop this branch.\n     |- Try 51 - 8 = 43. Evaluate 43 != 17, drop this branch.\n     |- Try 51 * 8 = 408. Evaluate 408 != 17, drop this branch.\n     |- Try 51 \/ 8 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 53 * 2 = 106. Add 106 to the number set. Current number set: [106, 8], target: 17, just two numbers left.\n     |- Try 106 + 8 = 114. Evaluate 114 != 17, drop this branch.\n     |- Try 106 - 8 = 98. Evaluate 98 != 17, drop this branch.\n     |- Try 106 * 8 = 848. Evaluate 848 != 17, drop this branch.\n     |- Try 106 \/ 8 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 53 \/ 2 = 26.5. 26.5 is a decimal, drop this branch.\n   |- Pick two numbers (53, 8) (numbers left: [2]). Try possible operations.\n    |- Try 53 + 8 = 61. Add 61 to the number set. Current number set: [61, 2], target: 17, just two numbers left.\n     |- Try 61 + 2 = 63. Evaluate 63 != 17, drop this branch.\n     |- Try 61 - 2 = 59. Evaluate 59 != 17, drop this branch.\n     |- Try 61 * 2 = 122. Evaluate 122 != 17, drop this branch.\n     |- Try 61 \/ 2 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 53 - 8 = 45. Add 45 to the number set. Current number set: [45, 2], target: 17, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 17, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 17, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 53 * 8 = 424. Add 424 to the number set. Current number set: [424, 2], target: 17, just two numbers left.\n     |- Try 424 + 2 = 426. Evaluate 426 != 17, drop this branch.\n     |- Try 424 - 2 = 422. Evaluate 422 != 17, drop this branch.\n     |- Try 424 * 2 = 848. Evaluate 848 != 17, drop this branch.\n     |- Try 424 \/ 2 = 212. Evaluate 212 != 17, drop this branch.\n    |- Try 53 \/ 8 = 6.6. 6.6 is a decimal, drop this branch.\n   |- Pick two numbers (2, 8) (numbers left: [53]). Try possible operations.\n    |- Try 8 + 2 = 10. Add 10 to the number set. Current number set: [10, 53], target: 17, just two numbers left.\n     |- Try 53 + 10 = 63. Evaluate 63 != 17, drop this branch.\n     |- Try 53 - 10 = 43. Evaluate 43 != 17, drop this branch.\n     |- Try 53 * 10 = 530. Evaluate 530 != 17, drop this branch.\n     |- Try 53 \/ 10 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 8 - 2 = 6. Add 6 to the number set. Current number set: [6, 53], target: 17, just two numbers left.\n     |- Try 53 + 6 = 59. Evaluate 59 != 17, drop this branch.\n     |- Try 53 - 6 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 53 * 6 = 318. Evaluate 318 != 17, drop this branch.\n     |- Try 53 \/ 6 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 8 * 2 = 16. Add 16 to the number set. Current number set: [16, 53], target: 17, just two numbers left.\n     |- Try 53 + 16 = 69. Evaluate 69 != 17, drop this branch.\n     |- Try 53 - 16 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 53 * 16 = 848. Evaluate 848 != 17, drop this branch.\n     |- Try 53 \/ 16 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 8 \/ 2 = 4. Add 4 to the number set. Current number set: [4, 53], target: 17, just two numbers left.\n     |- Try 53 + 4 = 57. Evaluate 57 != 17, drop this branch.\n     |- Try 53 - 4 = 49. Evaluate 49 != 17, drop this branch.\n     |- Try 53 * 4 = 212. Evaluate 212 != 17, drop this branch.\n     |- Try 53 \/ 4 = 13.2. 13.2 is a decimal, drop this branch.\n  |- Try 32 - 21 = 11. Add 11 to the number set. Current number set: [11, 2, 8], target: 17. Options for choosing two numbers: [(11, 2), (11, 8), (2, 8)].\n   |- Pick two numbers (11, 2) (numbers left: [8]). Try possible operations.\n    |- Try 11 + 2 = 13. Add 13 to the number set. Current number set: [13, 8], target: 17, just two numbers left.\n     |- Try 13 + 8 = 21. Evaluate 21 != 17, drop this branch.\n     |- Try 13 - 8 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 13 * 8 = 104. Evaluate 104 != 17, drop this branch.\n     |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 11 - 2 = 9. Add 9 to the number set. Current number set: [9, 8], target: 17, just two numbers left.\n     |- Try 9 + 8 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 9 + 8 = 17\nThe step before: 11 - 2 = 9\nThe first step: 32 - 21 = 11\n\nOutput the solution in the required format:\n<Solution>\n32 - 21 = 11\n11 - 2 = 9\n9 + 8 = 17\n<\/Solution>\n","item":{"nums":[21,32,2,8],"solution":["32 - 21 = 11","11 - 2 = 9","9 + 8 = 17"],"target":17}}
+{"instance_id":"countdown_2k_4","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 20, 40, 42]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [46, 20, 40, 42], target: 33. Options for choosing two numbers: [(46, 20), (46, 40), (46, 42), (20, 40), (20, 42), (40, 42)].\n |- Pick two numbers (46, 20) (numbers left: [40, 42]). Try possible operations.\n  |- Try 46 + 20 = 66. Add 66 to the number set. Current number set: [66, 40, 42], target: 33. Options for choosing two numbers: [(66, 40), (66, 42), (40, 42)].\n   |- Pick two numbers (66, 40) (numbers left: [42]). Try possible operations.\n    |- Try 66 + 40 = 106. Add 106 to the number set. Current number set: [106, 42], target: 33, just two numbers left.\n     |- Try 106 + 42 = 148. Evaluate 148 != 33, drop this branch.\n     |- Try 106 - 42 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 106 * 42 = 4452. 4452 exceeds the maximum intermediate result, drop this branch.\n     |- Try 106 \/ 42 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 66 - 40 = 26. Add 26 to the number set. Current number set: [26, 42], target: 33, just two numbers left.\n     |- Try 42 + 26 = 68. Evaluate 68 != 33, drop this branch.\n     |- Try 42 - 26 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 42 * 26 = 1092. Evaluate 1092 != 33, drop this branch.\n     |- Try 42 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 66 * 40 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n    |- Try 66 \/ 40 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (66, 42) (numbers left: [40]). Try possible operations.\n    |- Try 66 + 42 = 108. Add 108 to the number set. Current number set: [108, 40], target: 33, just two numbers left.\n     |- Try 108 + 40 = 148. Evaluate 148 != 33, drop this branch.\n     |- Try 108 - 40 = 68. Evaluate 68 != 33, drop this branch.\n     |- Try 108 * 40 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 40 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 66 - 42 = 24. Add 24 to the number set. Current number set: [24, 40], target: 33, just two numbers left.\n     |- Try 40 + 24 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 40 - 24 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 40 * 24 = 960. Evaluate 960 != 33, drop this branch.\n     |- Try 40 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 66 * 42 = 2772. 2772 exceeds the maximum intermediate result, drop this branch.\n    |- Try 66 \/ 42 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (40, 42) (numbers left: [66]). Try possible operations.\n    |- Try 42 + 40 = 82. Add 82 to the number set. Current number set: [82, 66], target: 33, just two numbers left.\n     |- Try 82 + 66 = 148. Evaluate 148 != 33, drop this branch.\n     |- Try 82 - 66 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 82 * 66 = 5412. 5412 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 66 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 - 40 = 2. Add 2 to the number set. Current number set: [2, 66], target: 33, just two numbers left.\n     |- Try 66 + 2 = 68. Evaluate 68 != 33, drop this branch.\n     |- Try 66 - 2 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 66 * 2 = 132. Evaluate 132 != 33, drop this branch.\n     |- Try 66 \/ 2 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 66 \/ 2 = 33\nThe step before: 42 - 40 = 2\nThe first step: 46 + 20 = 66\n\nOutput the solution in the required format:\n<Solution>\n46 + 20 = 66\n42 - 40 = 2\n66 \/ 2 = 33\n<\/Solution>\n","item":{"nums":[46,20,40,42],"solution":["46 + 20 = 66","42 - 40 = 2","66 \/ 2 = 33"],"target":33}}
+{"instance_id":"countdown_2k_5","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 6, 49, 16]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [22, 6, 49, 16], target: 28. Options for choosing two numbers: [(22, 6), (22, 49), (22, 16), (6, 49), (6, 16), (49, 16)].\n |- Pick two numbers (22, 6) (numbers left: [49, 16]). Try possible operations.\n  |- Try 22 + 6 = 28. Add 28 to the number set. Current number set: [28, 49, 16], target: 28. Options for choosing two numbers: [(28, 49), (28, 16), (49, 16)].\n   |- Pick two numbers (28, 49) (numbers left: [16]). Try possible operations.\n    |- Try 49 + 28 = 77. Add 77 to the number set. Current number set: [77, 16], target: 28, just two numbers left.\n     |- Try 77 + 16 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 77 - 16 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 77 * 16 = 1232. Evaluate 1232 != 28, drop this branch.\n     |- Try 77 \/ 16 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 49 - 28 = 21. Add 21 to the number set. Current number set: [21, 16], target: 28, just two numbers left.\n     |- Try 21 + 16 = 37. Evaluate 37 != 28, drop this branch.\n     |- Try 21 - 16 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 21 * 16 = 336. Evaluate 336 != 28, drop this branch.\n     |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 49 * 28 = 1372. Add 1372 to the number set. Current number set: [1372, 16], target: 28, just two numbers left.\n     |- Try 1372 + 16 = 1388. Evaluate 1388 != 28, drop this branch.\n     |- Try 1372 - 16 = 1356. Evaluate 1356 != 28, drop this branch.\n     |- Try 1372 * 16 = 21952. 21952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1372 \/ 16 = 85.8. 85.8 is a decimal, drop this branch.\n    |- Try 49 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (28, 16) (numbers left: [49]). Try possible operations.\n    |- Try 28 + 16 = 44. Add 44 to the number set. Current number set: [44, 49], target: 28, just two numbers left.\n     |- Try 49 + 44 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 49 - 44 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 49 * 44 = 2156. 2156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 16 = 12. Add 12 to the number set. Current number set: [12, 49], target: 28, just two numbers left.\n     |- Try 49 + 12 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 49 - 12 = 37. Evaluate 37 != 28, drop this branch.\n     |- Try 49 * 12 = 588. Evaluate 588 != 28, drop this branch.\n     |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 28 * 16 = 448. Add 448 to the number set. Current number set: [448, 49], target: 28, just two numbers left.\n     |- Try 448 + 49 = 497. Evaluate 497 != 28, drop this branch.\n     |- Try 448 - 49 = 399. Evaluate 399 != 28, drop this branch.\n     |- Try 448 * 49 = 21952. 21952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 448 \/ 49 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (49, 16) (numbers left: [28]). Try possible operations.\n    |- Try 49 + 16 = 65. Add 65 to the number set. Current number set: [65, 28], target: 28, just two numbers left.\n     |- Try 65 + 28 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 65 - 28 = 37. Evaluate 37 != 28, drop this branch.\n     |- Try 65 * 28 = 1820. Evaluate 1820 != 28, drop this branch.\n     |- Try 65 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 49 - 16 = 33. Add 33 to the number set. Current number set: [33, 28], target: 28, just two numbers left.\n     |- Try 33 + 28 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 33 - 28 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 33 * 28 = 924. Evaluate 924 != 28, drop this branch.\n     |- Try 33 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 * 16 = 784. Add 784 to the number set. Current number set: [784, 28], target: 28, just two numbers left.\n     |- Try 784 + 28 = 812. Evaluate 812 != 28, drop this branch.\n     |- Try 784 - 28 = 756. Evaluate 756 != 28, drop this branch.\n     |- Try 784 * 28 = 21952. 21952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 784 \/ 28 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 784 \/ 28 = 28\nThe step before: 49 * 16 = 784\nThe first step: 22 + 6 = 28\n\nOutput the solution in the required format:\n<Solution>\n22 + 6 = 28\n49 * 16 = 784\n784 \/ 28 = 28\n<\/Solution>\n","item":{"nums":[22,6,49,16],"solution":["22 + 6 = 28","49 * 16 = 784","784 \/ 28 = 28"],"target":28}}
+{"instance_id":"countdown_2k_6","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 14, 27, 25]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [4, 14, 27, 25], target: 36. Options for choosing two numbers: [(4, 14), (4, 27), (4, 25), (14, 27), (14, 25), (27, 25)].\n |- Pick two numbers (4, 14) (numbers left: [27, 25]). Try possible operations.\n  |- Try 14 + 4 = 18. Add 18 to the number set. Current number set: [18, 27, 25], target: 36. Options for choosing two numbers: [(18, 27), (18, 25), (27, 25)].\n   |- Pick two numbers (18, 27) (numbers left: [25]). Try possible operations.\n    |- Try 27 + 18 = 45. Add 45 to the number set. Current number set: [45, 25], target: 36, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 36, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 36, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 36, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 27 - 18 = 9. Add 9 to the number set. Current number set: [9, 25], target: 36, just two numbers left.\n     |- Try 25 + 9 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 25 - 9 = 16. Evaluate 16 != 36, drop this branch.\n     |- Try 25 * 9 = 225. Evaluate 225 != 36, drop this branch.\n     |- Try 25 \/ 9 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 27 * 18 = 486. Add 486 to the number set. Current number set: [486, 25], target: 36, just two numbers left.\n     |- Try 486 + 25 = 511. Evaluate 511 != 36, drop this branch.\n     |- Try 486 - 25 = 461. Evaluate 461 != 36, drop this branch.\n     |- Try 486 * 25 = 12150. 12150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 486 \/ 25 = 19.4. 19.4 is a decimal, drop this branch.\n    |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 25) (numbers left: [27]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 27], target: 36, just two numbers left.\n     |- Try 43 + 27 = 70. Evaluate 70 != 36, drop this branch.\n     |- Try 43 - 27 = 16. Evaluate 16 != 36, drop this branch.\n     |- Try 43 * 27 = 1161. Evaluate 1161 != 36, drop this branch.\n     |- Try 43 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 27], target: 36, just two numbers left.\n     |- Try 27 + 7 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 27 - 7 = 20. Evaluate 20 != 36, drop this branch.\n     |- Try 27 * 7 = 189. Evaluate 189 != 36, drop this branch.\n     |- Try 27 \/ 7 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 27], target: 36, just two numbers left.\n     |- Try 450 + 27 = 477. Evaluate 477 != 36, drop this branch.\n     |- Try 450 - 27 = 423. Evaluate 423 != 36, drop this branch.\n     |- Try 450 * 27 = 12150. 12150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 27 = 16.7. 16.7 is a decimal, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (27, 25) (numbers left: [18]). Try possible operations.\n    |- Try 27 + 25 = 52. Add 52 to the number set. Current number set: [52, 18], target: 36, just two numbers left.\n     |- Try 52 + 18 = 70. Evaluate 70 != 36, drop this branch.\n     |- Try 52 - 18 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 52 * 18 = 936. Evaluate 936 != 36, drop this branch.\n     |- Try 52 \/ 18 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 27 - 25 = 2. Add 2 to the number set. Current number set: [2, 18], target: 36, just two numbers left.\n     |- Try 18 + 2 = 20. Evaluate 20 != 36, drop this branch.\n     |- Try 18 - 2 = 16. Evaluate 16 != 36, drop this branch.\n     |- Try 18 * 2 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 18 * 2 = 36\nThe step before: 27 - 25 = 2\nThe first step: 14 + 4 = 18\n\nOutput the solution in the required format:\n<Solution>\n14 + 4 = 18\n27 - 25 = 2\n18 * 2 = 36\n<\/Solution>\n","item":{"nums":[4,14,27,25],"solution":["14 + 4 = 18","27 - 25 = 2","18 * 2 = 36"],"target":36}}
+{"instance_id":"countdown_2k_7","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [25, 22, 43, 44]\nTarget: 47","reference_output":"# Search Procedure\nInitial number set: [25, 22, 43, 44], target: 47. Options for choosing two numbers: [(25, 22), (25, 43), (25, 44), (22, 43), (22, 44), (43, 44)].\n |- Pick two numbers (25, 22) (numbers left: [43, 44]). Try possible operations.\n  |- Try 25 + 22 = 47. Add 47 to the number set. Current number set: [47, 43, 44], target: 47. Options for choosing two numbers: [(47, 43), (47, 44), (43, 44)].\n   |- Pick two numbers (47, 43) (numbers left: [44]). Try possible operations.\n    |- Try 47 + 43 = 90. Add 90 to the number set. Current number set: [90, 44], target: 47, just two numbers left.\n     |- Try 90 + 44 = 134. Evaluate 134 != 47, drop this branch.\n     |- Try 90 - 44 = 46. Evaluate 46 != 47, drop this branch.\n     |- Try 90 * 44 = 3960. 3960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 44 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 47 - 43 = 4. Add 4 to the number set. Current number set: [4, 44], target: 47, just two numbers left.\n     |- Try 44 + 4 = 48. Evaluate 48 != 47, drop this branch.\n     |- Try 44 - 4 = 40. Evaluate 40 != 47, drop this branch.\n     |- Try 44 * 4 = 176. Evaluate 176 != 47, drop this branch.\n     |- Try 44 \/ 4 = 11. Evaluate 11 != 47, drop this branch.\n    |- Try 47 * 43 = 2021. 2021 exceeds the maximum intermediate result, drop this branch.\n    |- Try 47 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (47, 44) (numbers left: [43]). Try possible operations.\n    |- Try 47 + 44 = 91. Add 91 to the number set. Current number set: [91, 43], target: 47, just two numbers left.\n     |- Try 91 + 43 = 134. Evaluate 134 != 47, drop this branch.\n     |- Try 91 - 43 = 48. Evaluate 48 != 47, drop this branch.\n     |- Try 91 * 43 = 3913. 3913 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 43 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 47 - 44 = 3. Add 3 to the number set. Current number set: [3, 43], target: 47, just two numbers left.\n     |- Try 43 + 3 = 46. Evaluate 46 != 47, drop this branch.\n     |- Try 43 - 3 = 40. Evaluate 40 != 47, drop this branch.\n     |- Try 43 * 3 = 129. Evaluate 129 != 47, drop this branch.\n     |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 47 * 44 = 2068. 2068 exceeds the maximum intermediate result, drop this branch.\n    |- Try 47 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (43, 44) (numbers left: [47]). Try possible operations.\n    |- Try 44 + 43 = 87. Add 87 to the number set. Current number set: [87, 47], target: 47, just two numbers left.\n     |- Try 87 + 47 = 134. Evaluate 134 != 47, drop this branch.\n     |- Try 87 - 47 = 40. Evaluate 40 != 47, drop this branch.\n     |- Try 87 * 47 = 4089. 4089 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 47 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 - 43 = 1. Add 1 to the number set. Current number set: [1, 47], target: 47, just two numbers left.\n     |- Try 47 + 1 = 48. Evaluate 48 != 47, drop this branch.\n     |- Try 47 - 1 = 46. Evaluate 46 != 47, drop this branch.\n     |- Try 47 * 1 = 47. Evaluate 47 == 47, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 * 1 = 47\nThe step before: 44 - 43 = 1\nThe first step: 25 + 22 = 47\n\nOutput the solution in the required format:\n<Solution>\n25 + 22 = 47\n44 - 43 = 1\n47 * 1 = 47\n<\/Solution>\n","item":{"nums":[25,22,43,44],"solution":["25 + 22 = 47","44 - 43 = 1","47 * 1 = 47"],"target":47}}
+{"instance_id":"countdown_2k_8","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 28, 47, 38]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [30, 28, 47, 38], target: 11. Options for choosing two numbers: [(30, 28), (30, 47), (30, 38), (28, 47), (28, 38), (47, 38)].\n |- Pick two numbers (30, 28) (numbers left: [47, 38]). Try possible operations.\n  |- Try 30 + 28 = 58. Add 58 to the number set. Current number set: [58, 47, 38], target: 11. Options for choosing two numbers: [(58, 47), (58, 38), (47, 38)].\n   |- Pick two numbers (58, 47) (numbers left: [38]). Try possible operations.\n    |- Try 58 + 47 = 105. Add 105 to the number set. Current number set: [105, 38], target: 11, just two numbers left.\n     |- Try 105 + 38 = 143. Evaluate 143 != 11, drop this branch.\n     |- Try 105 - 38 = 67. Evaluate 67 != 11, drop this branch.\n     |- Try 105 * 38 = 3990. 3990 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 38 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 58 - 47 = 11. Add 11 to the number set. Current number set: [11, 38], target: 11, just two numbers left.\n     |- Try 38 + 11 = 49. Evaluate 49 != 11, drop this branch.\n     |- Try 38 - 11 = 27. Evaluate 27 != 11, drop this branch.\n     |- Try 38 * 11 = 418. Evaluate 418 != 11, drop this branch.\n     |- Try 38 \/ 11 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 58 * 47 = 2726. 2726 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (58, 38) (numbers left: [47]). Try possible operations.\n    |- Try 58 + 38 = 96. Add 96 to the number set. Current number set: [96, 47], target: 11, just two numbers left.\n     |- Try 96 + 47 = 143. Evaluate 143 != 11, drop this branch.\n     |- Try 96 - 47 = 49. Evaluate 49 != 11, drop this branch.\n     |- Try 96 * 47 = 4512. 4512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 47 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 58 - 38 = 20. Add 20 to the number set. Current number set: [20, 47], target: 11, just two numbers left.\n     |- Try 47 + 20 = 67. Evaluate 67 != 11, drop this branch.\n     |- Try 47 - 20 = 27. Evaluate 27 != 11, drop this branch.\n     |- Try 47 * 20 = 940. Evaluate 940 != 11, drop this branch.\n     |- Try 47 \/ 20 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 58 * 38 = 2204. 2204 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 38 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (47, 38) (numbers left: [58]). Try possible operations.\n    |- Try 47 + 38 = 85. Add 85 to the number set. Current number set: [85, 58], target: 11, just two numbers left.\n     |- Try 85 + 58 = 143. Evaluate 143 != 11, drop this branch.\n     |- Try 85 - 58 = 27. Evaluate 27 != 11, drop this branch.\n     |- Try 85 * 58 = 4930. 4930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 58 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 47 - 38 = 9. Add 9 to the number set. Current number set: [9, 58], target: 11, just two numbers left.\n     |- Try 58 + 9 = 67. Evaluate 67 != 11, drop this branch.\n     |- Try 58 - 9 = 49. Evaluate 49 != 11, drop this branch.\n     |- Try 58 * 9 = 522. Evaluate 522 != 11, drop this branch.\n     |- Try 58 \/ 9 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 47 * 38 = 1786. Add 1786 to the number set. Current number set: [1786, 58], target: 11, just two numbers left.\n     |- Try 1786 + 58 = 1844. Evaluate 1844 != 11, drop this branch.\n     |- Try 1786 - 58 = 1728. Evaluate 1728 != 11, drop this branch.\n     |- Try 1786 * 58 = 103588. 103588 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1786 \/ 58 = 30.8. 30.8 is a decimal, drop this branch.\n    |- Try 47 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 30 - 28 = 2. Add 2 to the number set. Current number set: [2, 47, 38], target: 11. Options for choosing two numbers: [(2, 47), (2, 38), (47, 38)].\n   |- Pick two numbers (2, 47) (numbers left: [38]). Try possible operations.\n    |- Try 47 + 2 = 49. Add 49 to the number set. Current number set: [49, 38], target: 11, just two numbers left.\n     |- Try 49 + 38 = 87. Evaluate 87 != 11, drop this branch.\n     |- Try 49 - 38 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 - 38 = 11\nThe step before: 47 + 2 = 49\nThe first step: 30 - 28 = 2\n\nOutput the solution in the required format:\n<Solution>\n30 - 28 = 2\n47 + 2 = 49\n49 - 38 = 11\n<\/Solution>\n","item":{"nums":[30,28,47,38],"solution":["30 - 28 = 2","47 + 2 = 49","49 - 38 = 11"],"target":11}}
+{"instance_id":"countdown_2k_9","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 3, 15, 19]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [19, 3, 15, 19], target: 50. Options for choosing two numbers: [(19, 3), (19, 15), (19, 19), (3, 15), (3, 19), (15, 19)].\n |- Pick two numbers (19, 3) (numbers left: [15, 19]). Try possible operations.\n  |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 15, 19], target: 50. Options for choosing two numbers: [(22, 15), (22, 19), (15, 19)].\n   |- Pick two numbers (22, 15) (numbers left: [19]). Try possible operations.\n    |- Try 22 + 15 = 37. Add 37 to the number set. Current number set: [37, 19], target: 50, just two numbers left.\n     |- Try 37 + 19 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 37 - 19 = 18. Evaluate 18 != 50, drop this branch.\n     |- Try 37 * 19 = 703. Evaluate 703 != 50, drop this branch.\n     |- Try 37 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 22 - 15 = 7. Add 7 to the number set. Current number set: [7, 19], target: 50, just two numbers left.\n     |- Try 19 + 7 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 19 - 7 = 12. Evaluate 12 != 50, drop this branch.\n     |- Try 19 * 7 = 133. Evaluate 133 != 50, drop this branch.\n     |- Try 19 \/ 7 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 22 * 15 = 330. Add 330 to the number set. Current number set: [330, 19], target: 50, just two numbers left.\n     |- Try 330 + 19 = 349. Evaluate 349 != 50, drop this branch.\n     |- Try 330 - 19 = 311. Evaluate 311 != 50, drop this branch.\n     |- Try 330 * 19 = 6270. 6270 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 19 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 19) (numbers left: [15]). Try possible operations.\n    |- Try 22 + 19 = 41. Add 41 to the number set. Current number set: [41, 15], target: 50, just two numbers left.\n     |- Try 41 + 15 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 41 - 15 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 41 * 15 = 615. Evaluate 615 != 50, drop this branch.\n     |- Try 41 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 22 - 19 = 3. Add 3 to the number set. Current number set: [3, 15], target: 50, just two numbers left.\n     |- Try 15 + 3 = 18. Evaluate 18 != 50, drop this branch.\n     |- Try 15 - 3 = 12. Evaluate 12 != 50, drop this branch.\n     |- Try 15 * 3 = 45. Evaluate 45 != 50, drop this branch.\n     |- Try 15 \/ 3 = 5. Evaluate 5 != 50, drop this branch.\n    |- Try 22 * 19 = 418. Add 418 to the number set. Current number set: [418, 15], target: 50, just two numbers left.\n     |- Try 418 + 15 = 433. Evaluate 433 != 50, drop this branch.\n     |- Try 418 - 15 = 403. Evaluate 403 != 50, drop this branch.\n     |- Try 418 * 15 = 6270. 6270 exceeds the maximum intermediate result, drop this branch.\n     |- Try 418 \/ 15 = 27.9. 27.9 is a decimal, drop this branch.\n    |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 19) (numbers left: [22]). Try possible operations.\n    |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 22], target: 50, just two numbers left.\n     |- Try 34 + 22 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 34 - 22 = 12. Evaluate 12 != 50, drop this branch.\n     |- Try 34 * 22 = 748. Evaluate 748 != 50, drop this branch.\n     |- Try 34 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 22], target: 50, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 50, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 50, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 19 * 15 = 285. Add 285 to the number set. Current number set: [285, 22], target: 50, just two numbers left.\n     |- Try 285 + 22 = 307. Evaluate 307 != 50, drop this branch.\n     |- Try 285 - 22 = 263. Evaluate 263 != 50, drop this branch.\n     |- Try 285 * 22 = 6270. 6270 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 22 = 13.0. 13.0 is a decimal, drop this branch.\n    |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 15, 19], target: 50. Options for choosing two numbers: [(16, 15), (16, 19), (15, 19)].\n   |- Pick two numbers (16, 15) (numbers left: [19]). Try possible operations.\n    |- Try 16 + 15 = 31. Add 31 to the number set. Current number set: [31, 19], target: 50, just two numbers left.\n     |- Try 31 + 19 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 + 19 = 50\nThe step before: 16 + 15 = 31\nThe first step: 19 - 3 = 16\n\nOutput the solution in the required format:\n<Solution>\n19 - 3 = 16\n16 + 15 = 31\n31 + 19 = 50\n<\/Solution>\n","item":{"nums":[19,3,15,19],"solution":["19 - 3 = 16","16 + 15 = 31","31 + 19 = 50"],"target":50}}
+{"instance_id":"countdown_2k_10","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 36, 24, 6]\nTarget: 40","reference_output":"# Search Procedure\nInitial number set: [26, 36, 24, 6], target: 40. Options for choosing two numbers: [(26, 36), (26, 24), (26, 6), (36, 24), (36, 6), (24, 6)].\n |- Pick two numbers (26, 36) (numbers left: [24, 6]). Try possible operations.\n  |- Try 36 + 26 = 62. Add 62 to the number set. Current number set: [62, 24, 6], target: 40. Options for choosing two numbers: [(62, 24), (62, 6), (24, 6)].\n   |- Pick two numbers (62, 24) (numbers left: [6]). Try possible operations.\n    |- Try 62 + 24 = 86. Add 86 to the number set. Current number set: [86, 6], target: 40, just two numbers left.\n     |- Try 86 + 6 = 92. Evaluate 92 != 40, drop this branch.\n     |- Try 86 - 6 = 80. Evaluate 80 != 40, drop this branch.\n     |- Try 86 * 6 = 516. Evaluate 516 != 40, drop this branch.\n     |- Try 86 \/ 6 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 62 - 24 = 38. Add 38 to the number set. Current number set: [38, 6], target: 40, just two numbers left.\n     |- Try 38 + 6 = 44. Evaluate 44 != 40, drop this branch.\n     |- Try 38 - 6 = 32. Evaluate 32 != 40, drop this branch.\n     |- Try 38 * 6 = 228. Evaluate 228 != 40, drop this branch.\n     |- Try 38 \/ 6 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 62 * 24 = 1488. Add 1488 to the number set. Current number set: [1488, 6], target: 40, just two numbers left.\n     |- Try 1488 + 6 = 1494. Evaluate 1494 != 40, drop this branch.\n     |- Try 1488 - 6 = 1482. Evaluate 1482 != 40, drop this branch.\n     |- Try 1488 * 6 = 8928. 8928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1488 \/ 6 = 248. Evaluate 248 != 40, drop this branch.\n    |- Try 62 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (62, 6) (numbers left: [24]). Try possible operations.\n    |- Try 62 + 6 = 68. Add 68 to the number set. Current number set: [68, 24], target: 40, just two numbers left.\n     |- Try 68 + 24 = 92. Evaluate 92 != 40, drop this branch.\n     |- Try 68 - 24 = 44. Evaluate 44 != 40, drop this branch.\n     |- Try 68 * 24 = 1632. Evaluate 1632 != 40, drop this branch.\n     |- Try 68 \/ 24 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 62 - 6 = 56. Add 56 to the number set. Current number set: [56, 24], target: 40, just two numbers left.\n     |- Try 56 + 24 = 80. Evaluate 80 != 40, drop this branch.\n     |- Try 56 - 24 = 32. Evaluate 32 != 40, drop this branch.\n     |- Try 56 * 24 = 1344. Evaluate 1344 != 40, drop this branch.\n     |- Try 56 \/ 24 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 62 * 6 = 372. Add 372 to the number set. Current number set: [372, 24], target: 40, just two numbers left.\n     |- Try 372 + 24 = 396. Evaluate 396 != 40, drop this branch.\n     |- Try 372 - 24 = 348. Evaluate 348 != 40, drop this branch.\n     |- Try 372 * 24 = 8928. 8928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 372 \/ 24 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 62 \/ 6 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (24, 6) (numbers left: [62]). Try possible operations.\n    |- Try 24 + 6 = 30. Add 30 to the number set. Current number set: [30, 62], target: 40, just two numbers left.\n     |- Try 62 + 30 = 92. Evaluate 92 != 40, drop this branch.\n     |- Try 62 - 30 = 32. Evaluate 32 != 40, drop this branch.\n     |- Try 62 * 30 = 1860. Evaluate 1860 != 40, drop this branch.\n     |- Try 62 \/ 30 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 24 - 6 = 18. Add 18 to the number set. Current number set: [18, 62], target: 40, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 40, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 40, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 40, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 24 * 6 = 144. Add 144 to the number set. Current number set: [144, 62], target: 40, just two numbers left.\n     |- Try 144 + 62 = 206. Evaluate 206 != 40, drop this branch.\n     |- Try 144 - 62 = 82. Evaluate 82 != 40, drop this branch.\n     |- Try 144 * 62 = 8928. 8928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 62 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 24 \/ 6 = 4. Add 4 to the number set. Current number set: [4, 62], target: 40, just two numbers left.\n     |- Try 62 + 4 = 66. Evaluate 66 != 40, drop this branch.\n     |- Try 62 - 4 = 58. Evaluate 58 != 40, drop this branch.\n     |- Try 62 * 4 = 248. Evaluate 248 != 40, drop this branch.\n     |- Try 62 \/ 4 = 15.5. 15.5 is a decimal, drop this branch.\n  |- Try 36 - 26 = 10. Add 10 to the number set. Current number set: [10, 24, 6], target: 40. Options for choosing two numbers: [(10, 24), (10, 6), (24, 6)].\n   |- Pick two numbers (10, 24) (numbers left: [6]). Try possible operations.\n    |- Try 24 + 10 = 34. Add 34 to the number set. Current number set: [34, 6], target: 40, just two numbers left.\n     |- Try 34 + 6 = 40. Evaluate 40 == 40, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 6 = 40\nThe step before: 24 + 10 = 34\nThe first step: 36 - 26 = 10\n\nOutput the solution in the required format:\n<Solution>\n36 - 26 = 10\n24 + 10 = 34\n34 + 6 = 40\n<\/Solution>\n","item":{"nums":[26,36,24,6],"solution":["36 - 26 = 10","24 + 10 = 34","34 + 6 = 40"],"target":40}}
+{"instance_id":"countdown_2k_11","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 16, 38, 21]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [23, 16, 38, 21], target: 10. Options for choosing two numbers: [(23, 16), (23, 38), (23, 21), (16, 38), (16, 21), (38, 21)].\n |- Pick two numbers (23, 16) (numbers left: [38, 21]). Try possible operations.\n  |- Try 23 + 16 = 39. Add 39 to the number set. Current number set: [39, 38, 21], target: 10. Options for choosing two numbers: [(39, 38), (39, 21), (38, 21)].\n   |- Pick two numbers (39, 38) (numbers left: [21]). Try possible operations.\n    |- Try 39 + 38 = 77. Add 77 to the number set. Current number set: [77, 21], target: 10, just two numbers left.\n     |- Try 77 + 21 = 98. Evaluate 98 != 10, drop this branch.\n     |- Try 77 - 21 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 77 * 21 = 1617. Evaluate 1617 != 10, drop this branch.\n     |- Try 77 \/ 21 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 39 - 38 = 1. Add 1 to the number set. Current number set: [1, 21], target: 10, just two numbers left.\n     |- Try 21 + 1 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 21 - 1 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 21 * 1 = 21. Evaluate 21 != 10, drop this branch.\n     |- Try 21 \/ 1 = 21. Evaluate 21 != 10, drop this branch.\n    |- Try 39 * 38 = 1482. Add 1482 to the number set. Current number set: [1482, 21], target: 10, just two numbers left.\n     |- Try 1482 + 21 = 1503. Evaluate 1503 != 10, drop this branch.\n     |- Try 1482 - 21 = 1461. Evaluate 1461 != 10, drop this branch.\n     |- Try 1482 * 21 = 31122. 31122 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1482 \/ 21 = 70.6. 70.6 is a decimal, drop this branch.\n    |- Try 39 \/ 38 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (39, 21) (numbers left: [38]). Try possible operations.\n    |- Try 39 + 21 = 60. Add 60 to the number set. Current number set: [60, 38], target: 10, just two numbers left.\n     |- Try 60 + 38 = 98. Evaluate 98 != 10, drop this branch.\n     |- Try 60 - 38 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 - 21 = 18. Add 18 to the number set. Current number set: [18, 38], target: 10, just two numbers left.\n     |- Try 38 + 18 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 38 - 18 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 38 * 18 = 684. Evaluate 684 != 10, drop this branch.\n     |- Try 38 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 39 * 21 = 819. Add 819 to the number set. Current number set: [819, 38], target: 10, just two numbers left.\n     |- Try 819 + 38 = 857. Evaluate 857 != 10, drop this branch.\n     |- Try 819 - 38 = 781. Evaluate 781 != 10, drop this branch.\n     |- Try 819 * 38 = 31122. 31122 exceeds the maximum intermediate result, drop this branch.\n     |- Try 819 \/ 38 = 21.6. 21.6 is a decimal, drop this branch.\n    |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (38, 21) (numbers left: [39]). Try possible operations.\n    |- Try 38 + 21 = 59. Add 59 to the number set. Current number set: [59, 39], target: 10, just two numbers left.\n     |- Try 59 + 39 = 98. Evaluate 98 != 10, drop this branch.\n     |- Try 59 - 39 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 59 * 39 = 2301. 2301 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 39 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 38 - 21 = 17. Add 17 to the number set. Current number set: [17, 39], target: 10, just two numbers left.\n     |- Try 39 + 17 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 39 - 17 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 39 * 17 = 663. Evaluate 663 != 10, drop this branch.\n     |- Try 39 \/ 17 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 38 * 21 = 798. Add 798 to the number set. Current number set: [798, 39], target: 10, just two numbers left.\n     |- Try 798 + 39 = 837. Evaluate 837 != 10, drop this branch.\n     |- Try 798 - 39 = 759. Evaluate 759 != 10, drop this branch.\n     |- Try 798 * 39 = 31122. 31122 exceeds the maximum intermediate result, drop this branch.\n     |- Try 798 \/ 39 = 20.5. 20.5 is a decimal, drop this branch.\n    |- Try 38 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 23 - 16 = 7. Add 7 to the number set. Current number set: [7, 38, 21], target: 10. Options for choosing two numbers: [(7, 38), (7, 21), (38, 21)].\n   |- Pick two numbers (7, 38) (numbers left: [21]). Try possible operations.\n    |- Try 38 + 7 = 45. Add 45 to the number set. Current number set: [45, 21], target: 10, just two numbers left.\n     |- Try 45 + 21 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 45 - 21 = 24. Evaluate 24 != 10, drop this branch.\n     |- Try 45 * 21 = 945. Evaluate 945 != 10, drop this branch.\n     |- Try 45 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 38 - 7 = 31. Add 31 to the number set. Current number set: [31, 21], target: 10, just two numbers left.\n     |- Try 31 + 21 = 52. Evaluate 52 != 10, drop this branch.\n     |- Try 31 - 21 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 - 21 = 10\nThe step before: 38 - 7 = 31\nThe first step: 23 - 16 = 7\n\nOutput the solution in the required format:\n<Solution>\n23 - 16 = 7\n38 - 7 = 31\n31 - 21 = 10\n<\/Solution>\n","item":{"nums":[23,16,38,21],"solution":["23 - 16 = 7","38 - 7 = 31","31 - 21 = 10"],"target":10}}
+{"instance_id":"countdown_2k_12","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 17, 4, 9]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [12, 17, 4, 9], target: 11. Options for choosing two numbers: [(12, 17), (12, 4), (12, 9), (17, 4), (17, 9), (4, 9)].\n |- Pick two numbers (12, 17) (numbers left: [4, 9]). Try possible operations.\n  |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 4, 9], target: 11. Options for choosing two numbers: [(29, 4), (29, 9), (4, 9)].\n   |- Pick two numbers (29, 4) (numbers left: [9]). Try possible operations.\n    |- Try 29 + 4 = 33. Add 33 to the number set. Current number set: [33, 9], target: 11, just two numbers left.\n     |- Try 33 + 9 = 42. Evaluate 42 != 11, drop this branch.\n     |- Try 33 - 9 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 33 * 9 = 297. Evaluate 297 != 11, drop this branch.\n     |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 29 - 4 = 25. Add 25 to the number set. Current number set: [25, 9], target: 11, just two numbers left.\n     |- Try 25 + 9 = 34. Evaluate 34 != 11, drop this branch.\n     |- Try 25 - 9 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 25 * 9 = 225. Evaluate 225 != 11, drop this branch.\n     |- Try 25 \/ 9 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 29 * 4 = 116. Add 116 to the number set. Current number set: [116, 9], target: 11, just two numbers left.\n     |- Try 116 + 9 = 125. Evaluate 125 != 11, drop this branch.\n     |- Try 116 - 9 = 107. Evaluate 107 != 11, drop this branch.\n     |- Try 116 * 9 = 1044. Evaluate 1044 != 11, drop this branch.\n     |- Try 116 \/ 9 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 29 \/ 4 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 9) (numbers left: [4]). Try possible operations.\n    |- Try 29 + 9 = 38. Add 38 to the number set. Current number set: [38, 4], target: 11, just two numbers left.\n     |- Try 38 + 4 = 42. Evaluate 42 != 11, drop this branch.\n     |- Try 38 - 4 = 34. Evaluate 34 != 11, drop this branch.\n     |- Try 38 * 4 = 152. Evaluate 152 != 11, drop this branch.\n     |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 29 - 9 = 20. Add 20 to the number set. Current number set: [20, 4], target: 11, just two numbers left.\n     |- Try 20 + 4 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 20 - 4 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 20 * 4 = 80. Evaluate 80 != 11, drop this branch.\n     |- Try 20 \/ 4 = 5. Evaluate 5 != 11, drop this branch.\n    |- Try 29 * 9 = 261. Add 261 to the number set. Current number set: [261, 4], target: 11, just two numbers left.\n     |- Try 261 + 4 = 265. Evaluate 265 != 11, drop this branch.\n     |- Try 261 - 4 = 257. Evaluate 257 != 11, drop this branch.\n     |- Try 261 * 4 = 1044. Evaluate 1044 != 11, drop this branch.\n     |- Try 261 \/ 4 = 65.2. 65.2 is a decimal, drop this branch.\n    |- Try 29 \/ 9 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (4, 9) (numbers left: [29]). Try possible operations.\n    |- Try 9 + 4 = 13. Add 13 to the number set. Current number set: [13, 29], target: 11, just two numbers left.\n     |- Try 29 + 13 = 42. Evaluate 42 != 11, drop this branch.\n     |- Try 29 - 13 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 29 * 13 = 377. Evaluate 377 != 11, drop this branch.\n     |- Try 29 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 9 - 4 = 5. Add 5 to the number set. Current number set: [5, 29], target: 11, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 11, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 11, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 9 * 4 = 36. Add 36 to the number set. Current number set: [36, 29], target: 11, just two numbers left.\n     |- Try 36 + 29 = 65. Evaluate 65 != 11, drop this branch.\n     |- Try 36 - 29 = 7. Evaluate 7 != 11, drop this branch.\n     |- Try 36 * 29 = 1044. Evaluate 1044 != 11, drop this branch.\n     |- Try 36 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 4, 9], target: 11. Options for choosing two numbers: [(5, 4), (5, 9), (4, 9)].\n   |- Pick two numbers (5, 4) (numbers left: [9]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 9], target: 11, just two numbers left.\n     |- Try 9 + 9 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 9 - 9 = 0. Evaluate 0 != 11, drop this branch.\n     |- Try 9 * 9 = 81. Evaluate 81 != 11, drop this branch.\n     |- Try 9 \/ 9 = 1. Evaluate 1 != 11, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 9], target: 11, just two numbers left.\n     |- Try 9 + 1 = 10. Evaluate 10 != 11, drop this branch.\n     |- Try 9 - 1 = 8. Evaluate 8 != 11, drop this branch.\n     |- Try 9 * 1 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 9 \/ 1 = 9. Evaluate 9 != 11, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 9], target: 11, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 11, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 - 9 = 11\nThe step before: 5 * 4 = 20\nThe first step: 17 - 12 = 5\n\nOutput the solution in the required format:\n<Solution>\n17 - 12 = 5\n5 * 4 = 20\n20 - 9 = 11\n<\/Solution>\n","item":{"nums":[12,17,4,9],"solution":["17 - 12 = 5","5 * 4 = 20","20 - 9 = 11"],"target":11}}
+{"instance_id":"countdown_2k_13","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 44, 44, 38]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [19, 44, 44, 38], target: 31. Options for choosing two numbers: [(19, 44), (19, 44), (19, 38), (44, 44), (44, 38), (44, 38)].\n |- Pick two numbers (19, 44) (numbers left: [44, 38]). Try possible operations.\n  |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 44, 38], target: 31. Options for choosing two numbers: [(63, 44), (63, 38), (44, 38)].\n   |- Pick two numbers (63, 44) (numbers left: [38]). Try possible operations.\n    |- Try 63 + 44 = 107. Add 107 to the number set. Current number set: [107, 38], target: 31, just two numbers left.\n     |- Try 107 + 38 = 145. Evaluate 145 != 31, drop this branch.\n     |- Try 107 - 38 = 69. Evaluate 69 != 31, drop this branch.\n     |- Try 107 * 38 = 4066. 4066 exceeds the maximum intermediate result, drop this branch.\n     |- Try 107 \/ 38 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 63 - 44 = 19. Add 19 to the number set. Current number set: [19, 38], target: 31, just two numbers left.\n     |- Try 38 + 19 = 57. Evaluate 57 != 31, drop this branch.\n     |- Try 38 - 19 = 19. Evaluate 19 != 31, drop this branch.\n     |- Try 38 * 19 = 722. Evaluate 722 != 31, drop this branch.\n     |- Try 38 \/ 19 = 2. Evaluate 2 != 31, drop this branch.\n    |- Try 63 * 44 = 2772. 2772 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (63, 38) (numbers left: [44]). Try possible operations.\n    |- Try 63 + 38 = 101. Add 101 to the number set. Current number set: [101, 44], target: 31, just two numbers left.\n     |- Try 101 + 44 = 145. Evaluate 145 != 31, drop this branch.\n     |- Try 101 - 44 = 57. Evaluate 57 != 31, drop this branch.\n     |- Try 101 * 44 = 4444. 4444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 44 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 63 - 38 = 25. Add 25 to the number set. Current number set: [25, 44], target: 31, just two numbers left.\n     |- Try 44 + 25 = 69. Evaluate 69 != 31, drop this branch.\n     |- Try 44 - 25 = 19. Evaluate 19 != 31, drop this branch.\n     |- Try 44 * 25 = 1100. Evaluate 1100 != 31, drop this branch.\n     |- Try 44 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 63 * 38 = 2394. 2394 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 38 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (44, 38) (numbers left: [63]). Try possible operations.\n    |- Try 44 + 38 = 82. Add 82 to the number set. Current number set: [82, 63], target: 31, just two numbers left.\n     |- Try 82 + 63 = 145. Evaluate 145 != 31, drop this branch.\n     |- Try 82 - 63 = 19. Evaluate 19 != 31, drop this branch.\n     |- Try 82 * 63 = 5166. 5166 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 63 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 44 - 38 = 6. Add 6 to the number set. Current number set: [6, 63], target: 31, just two numbers left.\n     |- Try 63 + 6 = 69. Evaluate 69 != 31, drop this branch.\n     |- Try 63 - 6 = 57. Evaluate 57 != 31, drop this branch.\n     |- Try 63 * 6 = 378. Evaluate 378 != 31, drop this branch.\n     |- Try 63 \/ 6 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 44 * 38 = 1672. Add 1672 to the number set. Current number set: [1672, 63], target: 31, just two numbers left.\n     |- Try 1672 + 63 = 1735. Evaluate 1735 != 31, drop this branch.\n     |- Try 1672 - 63 = 1609. Evaluate 1609 != 31, drop this branch.\n     |- Try 1672 * 63 = 105336. 105336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1672 \/ 63 = 26.5. 26.5 is a decimal, drop this branch.\n    |- Try 44 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 44, 38], target: 31. Options for choosing two numbers: [(25, 44), (25, 38), (44, 38)].\n   |- Pick two numbers (25, 44) (numbers left: [38]). Try possible operations.\n    |- Try 44 + 25 = 69. Add 69 to the number set. Current number set: [69, 38], target: 31, just two numbers left.\n     |- Try 69 + 38 = 107. Evaluate 107 != 31, drop this branch.\n     |- Try 69 - 38 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 69 - 38 = 31\nThe step before: 44 + 25 = 69\nThe first step: 44 - 19 = 25\n\nOutput the solution in the required format:\n<Solution>\n44 - 19 = 25\n44 + 25 = 69\n69 - 38 = 31\n<\/Solution>\n","item":{"nums":[19,44,44,38],"solution":["44 - 19 = 25","44 + 25 = 69","69 - 38 = 31"],"target":31}}
+{"instance_id":"countdown_2k_14","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 8, 26, 2]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [19, 8, 26, 2], target: 14. Options for choosing two numbers: [(19, 8), (19, 26), (19, 2), (8, 26), (8, 2), (26, 2)].\n |- Pick two numbers (19, 8) (numbers left: [26, 2]). Try possible operations.\n  |- Try 19 + 8 = 27. Add 27 to the number set. Current number set: [27, 26, 2], target: 14. Options for choosing two numbers: [(27, 26), (27, 2), (26, 2)].\n   |- Pick two numbers (27, 26) (numbers left: [2]). Try possible operations.\n    |- Try 27 + 26 = 53. Add 53 to the number set. Current number set: [53, 2], target: 14, just two numbers left.\n     |- Try 53 + 2 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 53 - 2 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 53 * 2 = 106. Evaluate 106 != 14, drop this branch.\n     |- Try 53 \/ 2 = 26.5. 26.5 is a decimal, drop this branch.\n    |- Try 27 - 26 = 1. Add 1 to the number set. Current number set: [1, 2], target: 14, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 14, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 27 * 26 = 702. Add 702 to the number set. Current number set: [702, 2], target: 14, just two numbers left.\n     |- Try 702 + 2 = 704. Evaluate 704 != 14, drop this branch.\n     |- Try 702 - 2 = 700. Evaluate 700 != 14, drop this branch.\n     |- Try 702 * 2 = 1404. Evaluate 1404 != 14, drop this branch.\n     |- Try 702 \/ 2 = 351. Evaluate 351 != 14, drop this branch.\n    |- Try 27 \/ 26 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (27, 2) (numbers left: [26]). Try possible operations.\n    |- Try 27 + 2 = 29. Add 29 to the number set. Current number set: [29, 26], target: 14, just two numbers left.\n     |- Try 29 + 26 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 29 - 26 = 3. Evaluate 3 != 14, drop this branch.\n     |- Try 29 * 26 = 754. Evaluate 754 != 14, drop this branch.\n     |- Try 29 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 2 = 25. Add 25 to the number set. Current number set: [25, 26], target: 14, just two numbers left.\n     |- Try 26 + 25 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 26 - 25 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 26 * 25 = 650. Evaluate 650 != 14, drop this branch.\n     |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 27 * 2 = 54. Add 54 to the number set. Current number set: [54, 26], target: 14, just two numbers left.\n     |- Try 54 + 26 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 54 - 26 = 28. Evaluate 28 != 14, drop this branch.\n     |- Try 54 * 26 = 1404. Evaluate 1404 != 14, drop this branch.\n     |- Try 54 \/ 26 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (26, 2) (numbers left: [27]). Try possible operations.\n    |- Try 26 + 2 = 28. Add 28 to the number set. Current number set: [28, 27], target: 14, just two numbers left.\n     |- Try 28 + 27 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 28 - 27 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 28 * 27 = 756. Evaluate 756 != 14, drop this branch.\n     |- Try 28 \/ 27 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 26 - 2 = 24. Add 24 to the number set. Current number set: [24, 27], target: 14, just two numbers left.\n     |- Try 27 + 24 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 27 - 24 = 3. Evaluate 3 != 14, drop this branch.\n     |- Try 27 * 24 = 648. Evaluate 648 != 14, drop this branch.\n     |- Try 27 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 * 2 = 52. Add 52 to the number set. Current number set: [52, 27], target: 14, just two numbers left.\n     |- Try 52 + 27 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 52 - 27 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 52 * 27 = 1404. Evaluate 1404 != 14, drop this branch.\n     |- Try 52 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 26 \/ 2 = 13. Add 13 to the number set. Current number set: [13, 27], target: 14, just two numbers left.\n     |- Try 27 + 13 = 40. Evaluate 40 != 14, drop this branch.\n     |- Try 27 - 13 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 - 13 = 14\nThe step before: 26 \/ 2 = 13\nThe first step: 19 + 8 = 27\n\nOutput the solution in the required format:\n<Solution>\n19 + 8 = 27\n26 \/ 2 = 13\n27 - 13 = 14\n<\/Solution>\n","item":{"nums":[19,8,26,2],"solution":["19 + 8 = 27","26 \/ 2 = 13","27 - 13 = 14"],"target":14}}
+{"instance_id":"countdown_2k_15","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 33, 10, 4]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [31, 33, 10, 4], target: 48. Options for choosing two numbers: [(31, 33), (31, 10), (31, 4), (33, 10), (33, 4), (10, 4)].\n |- Pick two numbers (31, 33) (numbers left: [10, 4]). Try possible operations.\n  |- Try 33 + 31 = 64. Add 64 to the number set. Current number set: [64, 10, 4], target: 48. Options for choosing two numbers: [(64, 10), (64, 4), (10, 4)].\n   |- Pick two numbers (64, 10) (numbers left: [4]). Try possible operations.\n    |- Try 64 + 10 = 74. Add 74 to the number set. Current number set: [74, 4], target: 48, just two numbers left.\n     |- Try 74 + 4 = 78. Evaluate 78 != 48, drop this branch.\n     |- Try 74 - 4 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 74 * 4 = 296. Evaluate 296 != 48, drop this branch.\n     |- Try 74 \/ 4 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 64 - 10 = 54. Add 54 to the number set. Current number set: [54, 4], target: 48, just two numbers left.\n     |- Try 54 + 4 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 54 - 4 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 54 * 4 = 216. Evaluate 216 != 48, drop this branch.\n     |- Try 54 \/ 4 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 64 * 10 = 640. Add 640 to the number set. Current number set: [640, 4], target: 48, just two numbers left.\n     |- Try 640 + 4 = 644. Evaluate 644 != 48, drop this branch.\n     |- Try 640 - 4 = 636. Evaluate 636 != 48, drop this branch.\n     |- Try 640 * 4 = 2560. 2560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 4 = 160. Evaluate 160 != 48, drop this branch.\n    |- Try 64 \/ 10 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (64, 4) (numbers left: [10]). Try possible operations.\n    |- Try 64 + 4 = 68. Add 68 to the number set. Current number set: [68, 10], target: 48, just two numbers left.\n     |- Try 68 + 10 = 78. Evaluate 78 != 48, drop this branch.\n     |- Try 68 - 10 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 68 * 10 = 680. Evaluate 680 != 48, drop this branch.\n     |- Try 68 \/ 10 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 64 - 4 = 60. Add 60 to the number set. Current number set: [60, 10], target: 48, just two numbers left.\n     |- Try 60 + 10 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 60 - 10 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 60 * 10 = 600. Evaluate 600 != 48, drop this branch.\n     |- Try 60 \/ 10 = 6. Evaluate 6 != 48, drop this branch.\n    |- Try 64 * 4 = 256. Add 256 to the number set. Current number set: [256, 10], target: 48, just two numbers left.\n     |- Try 256 + 10 = 266. Evaluate 266 != 48, drop this branch.\n     |- Try 256 - 10 = 246. Evaluate 246 != 48, drop this branch.\n     |- Try 256 * 10 = 2560. 2560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 10 = 25.6. 25.6 is a decimal, drop this branch.\n    |- Try 64 \/ 4 = 16. Add 16 to the number set. Current number set: [16, 10], target: 48, just two numbers left.\n     |- Try 16 + 10 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 16 - 10 = 6. Evaluate 6 != 48, drop this branch.\n     |- Try 16 * 10 = 160. Evaluate 160 != 48, drop this branch.\n     |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (10, 4) (numbers left: [64]). Try possible operations.\n    |- Try 10 + 4 = 14. Add 14 to the number set. Current number set: [14, 64], target: 48, just two numbers left.\n     |- Try 64 + 14 = 78. Evaluate 78 != 48, drop this branch.\n     |- Try 64 - 14 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 64 * 14 = 896. Evaluate 896 != 48, drop this branch.\n     |- Try 64 \/ 14 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 10 - 4 = 6. Add 6 to the number set. Current number set: [6, 64], target: 48, just two numbers left.\n     |- Try 64 + 6 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 64 - 6 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 64 * 6 = 384. Evaluate 384 != 48, drop this branch.\n     |- Try 64 \/ 6 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 10 * 4 = 40. Add 40 to the number set. Current number set: [40, 64], target: 48, just two numbers left.\n     |- Try 64 + 40 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 64 - 40 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 64 * 40 = 2560. 2560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 40 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 33 - 31 = 2. Add 2 to the number set. Current number set: [2, 10, 4], target: 48. Options for choosing two numbers: [(2, 10), (2, 4), (10, 4)].\n   |- Pick two numbers (2, 10) (numbers left: [4]). Try possible operations.\n    |- Try 10 + 2 = 12. Add 12 to the number set. Current number set: [12, 4], target: 48, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 48, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 48, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 12 * 4 = 48\nThe step before: 10 + 2 = 12\nThe first step: 33 - 31 = 2\n\nOutput the solution in the required format:\n<Solution>\n33 - 31 = 2\n10 + 2 = 12\n12 * 4 = 48\n<\/Solution>\n","item":{"nums":[31,33,10,4],"solution":["33 - 31 = 2","10 + 2 = 12","12 * 4 = 48"],"target":48}}
+{"instance_id":"countdown_2k_16","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 9, 10, 5]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [15, 9, 10, 5], target: 21. Options for choosing two numbers: [(15, 9), (15, 10), (15, 5), (9, 10), (9, 5), (10, 5)].\n |- Pick two numbers (15, 9) (numbers left: [10, 5]). Try possible operations.\n  |- Try 15 + 9 = 24. Add 24 to the number set. Current number set: [24, 10, 5], target: 21. Options for choosing two numbers: [(24, 10), (24, 5), (10, 5)].\n   |- Pick two numbers (24, 10) (numbers left: [5]). Try possible operations.\n    |- Try 24 + 10 = 34. Add 34 to the number set. Current number set: [34, 5], target: 21, just two numbers left.\n     |- Try 34 + 5 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 34 - 5 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 34 * 5 = 170. Evaluate 170 != 21, drop this branch.\n     |- Try 34 \/ 5 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 24 - 10 = 14. Add 14 to the number set. Current number set: [14, 5], target: 21, just two numbers left.\n     |- Try 14 + 5 = 19. Evaluate 19 != 21, drop this branch.\n     |- Try 14 - 5 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 14 * 5 = 70. Evaluate 70 != 21, drop this branch.\n     |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 24 * 10 = 240. Add 240 to the number set. Current number set: [240, 5], target: 21, just two numbers left.\n     |- Try 240 + 5 = 245. Evaluate 245 != 21, drop this branch.\n     |- Try 240 - 5 = 235. Evaluate 235 != 21, drop this branch.\n     |- Try 240 * 5 = 1200. Evaluate 1200 != 21, drop this branch.\n     |- Try 240 \/ 5 = 48. Evaluate 48 != 21, drop this branch.\n    |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (24, 5) (numbers left: [10]). Try possible operations.\n    |- Try 24 + 5 = 29. Add 29 to the number set. Current number set: [29, 10], target: 21, just two numbers left.\n     |- Try 29 + 10 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 29 - 10 = 19. Evaluate 19 != 21, drop this branch.\n     |- Try 29 * 10 = 290. Evaluate 290 != 21, drop this branch.\n     |- Try 29 \/ 10 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 24 - 5 = 19. Add 19 to the number set. Current number set: [19, 10], target: 21, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 21, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 24 * 5 = 120. Add 120 to the number set. Current number set: [120, 10], target: 21, just two numbers left.\n     |- Try 120 + 10 = 130. Evaluate 130 != 21, drop this branch.\n     |- Try 120 - 10 = 110. Evaluate 110 != 21, drop this branch.\n     |- Try 120 * 10 = 1200. Evaluate 1200 != 21, drop this branch.\n     |- Try 120 \/ 10 = 12. Evaluate 12 != 21, drop this branch.\n    |- Try 24 \/ 5 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (10, 5) (numbers left: [24]). Try possible operations.\n    |- Try 10 + 5 = 15. Add 15 to the number set. Current number set: [15, 24], target: 21, just two numbers left.\n     |- Try 24 + 15 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 24 - 15 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 24 * 15 = 360. Evaluate 360 != 21, drop this branch.\n     |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 10 - 5 = 5. Add 5 to the number set. Current number set: [5, 24], target: 21, just two numbers left.\n     |- Try 24 + 5 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 24 - 5 = 19. Evaluate 19 != 21, drop this branch.\n     |- Try 24 * 5 = 120. Evaluate 120 != 21, drop this branch.\n     |- Try 24 \/ 5 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 10 * 5 = 50. Add 50 to the number set. Current number set: [50, 24], target: 21, just two numbers left.\n     |- Try 50 + 24 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 50 - 24 = 26. Evaluate 26 != 21, drop this branch.\n     |- Try 50 * 24 = 1200. Evaluate 1200 != 21, drop this branch.\n     |- Try 50 \/ 24 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 10 \/ 5 = 2. Add 2 to the number set. Current number set: [2, 24], target: 21, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 21, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 21, drop this branch.\n  |- Try 15 - 9 = 6. Add 6 to the number set. Current number set: [6, 10, 5], target: 21. Options for choosing two numbers: [(6, 10), (6, 5), (10, 5)].\n   |- Pick two numbers (6, 10) (numbers left: [5]). Try possible operations.\n    |- Try 10 + 6 = 16. Add 16 to the number set. Current number set: [16, 5], target: 21, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 5 = 21\nThe step before: 10 + 6 = 16\nThe first step: 15 - 9 = 6\n\nOutput the solution in the required format:\n<Solution>\n15 - 9 = 6\n10 + 6 = 16\n16 + 5 = 21\n<\/Solution>\n","item":{"nums":[15,9,10,5],"solution":["15 - 9 = 6","10 + 6 = 16","16 + 5 = 21"],"target":21}}
+{"instance_id":"countdown_2k_17","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 42, 22, 10]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [46, 42, 22, 10], target: 16. Options for choosing two numbers: [(46, 42), (46, 22), (46, 10), (42, 22), (42, 10), (22, 10)].\n |- Pick two numbers (46, 42) (numbers left: [22, 10]). Try possible operations.\n  |- Try 46 + 42 = 88. Add 88 to the number set. Current number set: [88, 22, 10], target: 16. Options for choosing two numbers: [(88, 22), (88, 10), (22, 10)].\n   |- Pick two numbers (88, 22) (numbers left: [10]). Try possible operations.\n    |- Try 88 + 22 = 110. Add 110 to the number set. Current number set: [110, 10], target: 16, just two numbers left.\n     |- Try 110 + 10 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 110 - 10 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 110 * 10 = 1100. Evaluate 1100 != 16, drop this branch.\n     |- Try 110 \/ 10 = 11. Evaluate 11 != 16, drop this branch.\n    |- Try 88 - 22 = 66. Add 66 to the number set. Current number set: [66, 10], target: 16, just two numbers left.\n     |- Try 66 + 10 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 66 - 10 = 56. Evaluate 56 != 16, drop this branch.\n     |- Try 66 * 10 = 660. Evaluate 660 != 16, drop this branch.\n     |- Try 66 \/ 10 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 88 * 22 = 1936. Add 1936 to the number set. Current number set: [1936, 10], target: 16, just two numbers left.\n     |- Try 1936 + 10 = 1946. Evaluate 1946 != 16, drop this branch.\n     |- Try 1936 - 10 = 1926. Evaluate 1926 != 16, drop this branch.\n     |- Try 1936 * 10 = 19360. 19360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1936 \/ 10 = 193.6. 193.6 is a decimal, drop this branch.\n    |- Try 88 \/ 22 = 4. Add 4 to the number set. Current number set: [4, 10], target: 16, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 16, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 16, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (88, 10) (numbers left: [22]). Try possible operations.\n    |- Try 88 + 10 = 98. Add 98 to the number set. Current number set: [98, 22], target: 16, just two numbers left.\n     |- Try 98 + 22 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 98 - 22 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 98 * 22 = 2156. 2156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 22 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 88 - 10 = 78. Add 78 to the number set. Current number set: [78, 22], target: 16, just two numbers left.\n     |- Try 78 + 22 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 78 - 22 = 56. Evaluate 56 != 16, drop this branch.\n     |- Try 78 * 22 = 1716. Evaluate 1716 != 16, drop this branch.\n     |- Try 78 \/ 22 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 88 * 10 = 880. Add 880 to the number set. Current number set: [880, 22], target: 16, just two numbers left.\n     |- Try 880 + 22 = 902. Evaluate 902 != 16, drop this branch.\n     |- Try 880 - 22 = 858. Evaluate 858 != 16, drop this branch.\n     |- Try 880 * 22 = 19360. 19360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 880 \/ 22 = 40. Evaluate 40 != 16, drop this branch.\n    |- Try 88 \/ 10 = 8.8. 8.8 is a decimal, drop this branch.\n   |- Pick two numbers (22, 10) (numbers left: [88]). Try possible operations.\n    |- Try 22 + 10 = 32. Add 32 to the number set. Current number set: [32, 88], target: 16, just two numbers left.\n     |- Try 88 + 32 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 88 - 32 = 56. Evaluate 56 != 16, drop this branch.\n     |- Try 88 * 32 = 2816. 2816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 32 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 22 - 10 = 12. Add 12 to the number set. Current number set: [12, 88], target: 16, just two numbers left.\n     |- Try 88 + 12 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 88 - 12 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 88 * 12 = 1056. Evaluate 1056 != 16, drop this branch.\n     |- Try 88 \/ 12 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 22 * 10 = 220. Add 220 to the number set. Current number set: [220, 88], target: 16, just two numbers left.\n     |- Try 220 + 88 = 308. Evaluate 308 != 16, drop this branch.\n     |- Try 220 - 88 = 132. Evaluate 132 != 16, drop this branch.\n     |- Try 220 * 88 = 19360. 19360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 88 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 46 - 42 = 4. Add 4 to the number set. Current number set: [4, 22, 10], target: 16. Options for choosing two numbers: [(4, 22), (4, 10), (22, 10)].\n   |- Pick two numbers (4, 22) (numbers left: [10]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 10], target: 16, just two numbers left.\n     |- Try 26 + 10 = 36. Evaluate 36 != 16, drop this branch.\n     |- Try 26 - 10 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 - 10 = 16\nThe step before: 22 + 4 = 26\nThe first step: 46 - 42 = 4\n\nOutput the solution in the required format:\n<Solution>\n46 - 42 = 4\n22 + 4 = 26\n26 - 10 = 16\n<\/Solution>\n","item":{"nums":[46,42,22,10],"solution":["46 - 42 = 4","22 + 4 = 26","26 - 10 = 16"],"target":16}}
+{"instance_id":"countdown_2k_18","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [29, 40, 1, 6]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [29, 40, 1, 6], target: 18. Options for choosing two numbers: [(29, 40), (29, 1), (29, 6), (40, 1), (40, 6), (1, 6)].\n |- Pick two numbers (29, 40) (numbers left: [1, 6]). Try possible operations.\n  |- Try 40 + 29 = 69. Add 69 to the number set. Current number set: [69, 1, 6], target: 18. Options for choosing two numbers: [(69, 1), (69, 6), (1, 6)].\n   |- Pick two numbers (69, 1) (numbers left: [6]). Try possible operations.\n    |- Try 69 + 1 = 70. Add 70 to the number set. Current number set: [70, 6], target: 18, just two numbers left.\n     |- Try 70 + 6 = 76. Evaluate 76 != 18, drop this branch.\n     |- Try 70 - 6 = 64. Evaluate 64 != 18, drop this branch.\n     |- Try 70 * 6 = 420. Evaluate 420 != 18, drop this branch.\n     |- Try 70 \/ 6 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 69 - 1 = 68. Add 68 to the number set. Current number set: [68, 6], target: 18, just two numbers left.\n     |- Try 68 + 6 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 68 - 6 = 62. Evaluate 62 != 18, drop this branch.\n     |- Try 68 * 6 = 408. Evaluate 408 != 18, drop this branch.\n     |- Try 68 \/ 6 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 69 * 1 = 69. Add 69 to the number set. Current number set: [69, 6], target: 18, just two numbers left.\n     |- Try 69 + 6 = 75. Evaluate 75 != 18, drop this branch.\n     |- Try 69 - 6 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 69 * 6 = 414. Evaluate 414 != 18, drop this branch.\n     |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 69 \/ 1 = 69. Add 69 to the number set. Current number set: [69, 6], target: 18, just two numbers left.\n     |- Try 69 + 6 = 75. Evaluate 75 != 18, drop this branch.\n     |- Try 69 - 6 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 69 * 6 = 414. Evaluate 414 != 18, drop this branch.\n     |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (69, 6) (numbers left: [1]). Try possible operations.\n    |- Try 69 + 6 = 75. Add 75 to the number set. Current number set: [75, 1], target: 18, just two numbers left.\n     |- Try 75 + 1 = 76. Evaluate 76 != 18, drop this branch.\n     |- Try 75 - 1 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 75 * 1 = 75. Evaluate 75 != 18, drop this branch.\n     |- Try 75 \/ 1 = 75. Evaluate 75 != 18, drop this branch.\n    |- Try 69 - 6 = 63. Add 63 to the number set. Current number set: [63, 1], target: 18, just two numbers left.\n     |- Try 63 + 1 = 64. Evaluate 64 != 18, drop this branch.\n     |- Try 63 - 1 = 62. Evaluate 62 != 18, drop this branch.\n     |- Try 63 * 1 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 63 \/ 1 = 63. Evaluate 63 != 18, drop this branch.\n    |- Try 69 * 6 = 414. Add 414 to the number set. Current number set: [414, 1], target: 18, just two numbers left.\n     |- Try 414 + 1 = 415. Evaluate 415 != 18, drop this branch.\n     |- Try 414 - 1 = 413. Evaluate 413 != 18, drop this branch.\n     |- Try 414 * 1 = 414. Evaluate 414 != 18, drop this branch.\n     |- Try 414 \/ 1 = 414. Evaluate 414 != 18, drop this branch.\n    |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (1, 6) (numbers left: [69]). Try possible operations.\n    |- Try 6 + 1 = 7. Add 7 to the number set. Current number set: [7, 69], target: 18, just two numbers left.\n     |- Try 69 + 7 = 76. Evaluate 76 != 18, drop this branch.\n     |- Try 69 - 7 = 62. Evaluate 62 != 18, drop this branch.\n     |- Try 69 * 7 = 483. Evaluate 483 != 18, drop this branch.\n     |- Try 69 \/ 7 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 6 - 1 = 5. Add 5 to the number set. Current number set: [5, 69], target: 18, just two numbers left.\n     |- Try 69 + 5 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 69 - 5 = 64. Evaluate 64 != 18, drop this branch.\n     |- Try 69 * 5 = 345. Evaluate 345 != 18, drop this branch.\n     |- Try 69 \/ 5 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 6 * 1 = 6. Add 6 to the number set. Current number set: [6, 69], target: 18, just two numbers left.\n     |- Try 69 + 6 = 75. Evaluate 75 != 18, drop this branch.\n     |- Try 69 - 6 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 69 * 6 = 414. Evaluate 414 != 18, drop this branch.\n     |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 6 \/ 1 = 6. Add 6 to the number set. Current number set: [6, 69], target: 18, just two numbers left.\n     |- Try 69 + 6 = 75. Evaluate 75 != 18, drop this branch.\n     |- Try 69 - 6 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 69 * 6 = 414. Evaluate 414 != 18, drop this branch.\n     |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n  |- Try 40 - 29 = 11. Add 11 to the number set. Current number set: [11, 1, 6], target: 18. Options for choosing two numbers: [(11, 1), (11, 6), (1, 6)].\n   |- Pick two numbers (11, 1) (numbers left: [6]). Try possible operations.\n    |- Try 11 + 1 = 12. Add 12 to the number set. Current number set: [12, 6], target: 18, just two numbers left.\n     |- Try 12 + 6 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 12 + 6 = 18\nThe step before: 11 + 1 = 12\nThe first step: 40 - 29 = 11\n\nOutput the solution in the required format:\n<Solution>\n40 - 29 = 11\n11 + 1 = 12\n12 + 6 = 18\n<\/Solution>\n","item":{"nums":[29,40,1,6],"solution":["40 - 29 = 11","11 + 1 = 12","12 + 6 = 18"],"target":18}}
+{"instance_id":"countdown_2k_19","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [28, 39, 12, 35]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [28, 39, 12, 35], target: 35. Options for choosing two numbers: [(28, 39), (28, 12), (28, 35), (39, 12), (39, 35), (12, 35)].\n |- Pick two numbers (28, 39) (numbers left: [12, 35]). Try possible operations.\n  |- Try 39 + 28 = 67. Add 67 to the number set. Current number set: [67, 12, 35], target: 35. Options for choosing two numbers: [(67, 12), (67, 35), (12, 35)].\n   |- Pick two numbers (67, 12) (numbers left: [35]). Try possible operations.\n    |- Try 67 + 12 = 79. Add 79 to the number set. Current number set: [79, 35], target: 35, just two numbers left.\n     |- Try 79 + 35 = 114. Evaluate 114 != 35, drop this branch.\n     |- Try 79 - 35 = 44. Evaluate 44 != 35, drop this branch.\n     |- Try 79 * 35 = 2765. 2765 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 35 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 67 - 12 = 55. Add 55 to the number set. Current number set: [55, 35], target: 35, just two numbers left.\n     |- Try 55 + 35 = 90. Evaluate 90 != 35, drop this branch.\n     |- Try 55 - 35 = 20. Evaluate 20 != 35, drop this branch.\n     |- Try 55 * 35 = 1925. Evaluate 1925 != 35, drop this branch.\n     |- Try 55 \/ 35 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 67 * 12 = 804. Add 804 to the number set. Current number set: [804, 35], target: 35, just two numbers left.\n     |- Try 804 + 35 = 839. Evaluate 839 != 35, drop this branch.\n     |- Try 804 - 35 = 769. Evaluate 769 != 35, drop this branch.\n     |- Try 804 * 35 = 28140. 28140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 804 \/ 35 = 23.0. 23.0 is a decimal, drop this branch.\n    |- Try 67 \/ 12 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (67, 35) (numbers left: [12]). Try possible operations.\n    |- Try 67 + 35 = 102. Add 102 to the number set. Current number set: [102, 12], target: 35, just two numbers left.\n     |- Try 102 + 12 = 114. Evaluate 114 != 35, drop this branch.\n     |- Try 102 - 12 = 90. Evaluate 90 != 35, drop this branch.\n     |- Try 102 * 12 = 1224. Evaluate 1224 != 35, drop this branch.\n     |- Try 102 \/ 12 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 67 - 35 = 32. Add 32 to the number set. Current number set: [32, 12], target: 35, just two numbers left.\n     |- Try 32 + 12 = 44. Evaluate 44 != 35, drop this branch.\n     |- Try 32 - 12 = 20. Evaluate 20 != 35, drop this branch.\n     |- Try 32 * 12 = 384. Evaluate 384 != 35, drop this branch.\n     |- Try 32 \/ 12 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 67 * 35 = 2345. 2345 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 35 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (12, 35) (numbers left: [67]). Try possible operations.\n    |- Try 35 + 12 = 47. Add 47 to the number set. Current number set: [47, 67], target: 35, just two numbers left.\n     |- Try 67 + 47 = 114. Evaluate 114 != 35, drop this branch.\n     |- Try 67 - 47 = 20. Evaluate 20 != 35, drop this branch.\n     |- Try 67 * 47 = 3149. 3149 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 47 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 - 12 = 23. Add 23 to the number set. Current number set: [23, 67], target: 35, just two numbers left.\n     |- Try 67 + 23 = 90. Evaluate 90 != 35, drop this branch.\n     |- Try 67 - 23 = 44. Evaluate 44 != 35, drop this branch.\n     |- Try 67 * 23 = 1541. Evaluate 1541 != 35, drop this branch.\n     |- Try 67 \/ 23 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 35 * 12 = 420. Add 420 to the number set. Current number set: [420, 67], target: 35, just two numbers left.\n     |- Try 420 + 67 = 487. Evaluate 487 != 35, drop this branch.\n     |- Try 420 - 67 = 353. Evaluate 353 != 35, drop this branch.\n     |- Try 420 * 67 = 28140. 28140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 67 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 35 \/ 12 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 39 - 28 = 11. Add 11 to the number set. Current number set: [11, 12, 35], target: 35. Options for choosing two numbers: [(11, 12), (11, 35), (12, 35)].\n   |- Pick two numbers (11, 12) (numbers left: [35]). Try possible operations.\n    |- Try 12 + 11 = 23. Add 23 to the number set. Current number set: [23, 35], target: 35, just two numbers left.\n     |- Try 35 + 23 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 35 - 23 = 12. Evaluate 12 != 35, drop this branch.\n     |- Try 35 * 23 = 805. Evaluate 805 != 35, drop this branch.\n     |- Try 35 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 12 - 11 = 1. Add 1 to the number set. Current number set: [1, 35], target: 35, just two numbers left.\n     |- Try 35 + 1 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 35 - 1 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 35 * 1 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 * 1 = 35\nThe step before: 12 - 11 = 1\nThe first step: 39 - 28 = 11\n\nOutput the solution in the required format:\n<Solution>\n39 - 28 = 11\n12 - 11 = 1\n35 * 1 = 35\n<\/Solution>\n","item":{"nums":[28,39,12,35],"solution":["39 - 28 = 11","12 - 11 = 1","35 * 1 = 35"],"target":35}}
+{"instance_id":"countdown_2k_20","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 11, 2, 10]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [44, 11, 2, 10], target: 50. Options for choosing two numbers: [(44, 11), (44, 2), (44, 10), (11, 2), (11, 10), (2, 10)].\n |- Pick two numbers (44, 11) (numbers left: [2, 10]). Try possible operations.\n  |- Try 44 + 11 = 55. Add 55 to the number set. Current number set: [55, 2, 10], target: 50. Options for choosing two numbers: [(55, 2), (55, 10), (2, 10)].\n   |- Pick two numbers (55, 2) (numbers left: [10]). Try possible operations.\n    |- Try 55 + 2 = 57. Add 57 to the number set. Current number set: [57, 10], target: 50, just two numbers left.\n     |- Try 57 + 10 = 67. Evaluate 67 != 50, drop this branch.\n     |- Try 57 - 10 = 47. Evaluate 47 != 50, drop this branch.\n     |- Try 57 * 10 = 570. Evaluate 570 != 50, drop this branch.\n     |- Try 57 \/ 10 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 55 - 2 = 53. Add 53 to the number set. Current number set: [53, 10], target: 50, just two numbers left.\n     |- Try 53 + 10 = 63. Evaluate 63 != 50, drop this branch.\n     |- Try 53 - 10 = 43. Evaluate 43 != 50, drop this branch.\n     |- Try 53 * 10 = 530. Evaluate 530 != 50, drop this branch.\n     |- Try 53 \/ 10 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 55 * 2 = 110. Add 110 to the number set. Current number set: [110, 10], target: 50, just two numbers left.\n     |- Try 110 + 10 = 120. Evaluate 120 != 50, drop this branch.\n     |- Try 110 - 10 = 100. Evaluate 100 != 50, drop this branch.\n     |- Try 110 * 10 = 1100. Evaluate 1100 != 50, drop this branch.\n     |- Try 110 \/ 10 = 11. Evaluate 11 != 50, drop this branch.\n    |- Try 55 \/ 2 = 27.5. 27.5 is a decimal, drop this branch.\n   |- Pick two numbers (55, 10) (numbers left: [2]). Try possible operations.\n    |- Try 55 + 10 = 65. Add 65 to the number set. Current number set: [65, 2], target: 50, just two numbers left.\n     |- Try 65 + 2 = 67. Evaluate 67 != 50, drop this branch.\n     |- Try 65 - 2 = 63. Evaluate 63 != 50, drop this branch.\n     |- Try 65 * 2 = 130. Evaluate 130 != 50, drop this branch.\n     |- Try 65 \/ 2 = 32.5. 32.5 is a decimal, drop this branch.\n    |- Try 55 - 10 = 45. Add 45 to the number set. Current number set: [45, 2], target: 50, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 50, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 50, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 50, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 55 * 10 = 550. Add 550 to the number set. Current number set: [550, 2], target: 50, just two numbers left.\n     |- Try 550 + 2 = 552. Evaluate 552 != 50, drop this branch.\n     |- Try 550 - 2 = 548. Evaluate 548 != 50, drop this branch.\n     |- Try 550 * 2 = 1100. Evaluate 1100 != 50, drop this branch.\n     |- Try 550 \/ 2 = 275. Evaluate 275 != 50, drop this branch.\n    |- Try 55 \/ 10 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 10) (numbers left: [55]). Try possible operations.\n    |- Try 10 + 2 = 12. Add 12 to the number set. Current number set: [12, 55], target: 50, just two numbers left.\n     |- Try 55 + 12 = 67. Evaluate 67 != 50, drop this branch.\n     |- Try 55 - 12 = 43. Evaluate 43 != 50, drop this branch.\n     |- Try 55 * 12 = 660. Evaluate 660 != 50, drop this branch.\n     |- Try 55 \/ 12 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 10 - 2 = 8. Add 8 to the number set. Current number set: [8, 55], target: 50, just two numbers left.\n     |- Try 55 + 8 = 63. Evaluate 63 != 50, drop this branch.\n     |- Try 55 - 8 = 47. Evaluate 47 != 50, drop this branch.\n     |- Try 55 * 8 = 440. Evaluate 440 != 50, drop this branch.\n     |- Try 55 \/ 8 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 10 * 2 = 20. Add 20 to the number set. Current number set: [20, 55], target: 50, just two numbers left.\n     |- Try 55 + 20 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 55 - 20 = 35. Evaluate 35 != 50, drop this branch.\n     |- Try 55 * 20 = 1100. Evaluate 1100 != 50, drop this branch.\n     |- Try 55 \/ 20 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 10 \/ 2 = 5. Add 5 to the number set. Current number set: [5, 55], target: 50, just two numbers left.\n     |- Try 55 + 5 = 60. Evaluate 60 != 50, drop this branch.\n     |- Try 55 - 5 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 55 - 5 = 50\nThe step before: 10 \/ 2 = 5\nThe first step: 44 + 11 = 55\n\nOutput the solution in the required format:\n<Solution>\n44 + 11 = 55\n10 \/ 2 = 5\n55 - 5 = 50\n<\/Solution>\n","item":{"nums":[44,11,2,10],"solution":["44 + 11 = 55","10 \/ 2 = 5","55 - 5 = 50"],"target":50}}
+{"instance_id":"countdown_2k_21","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [36, 18, 9, 41]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [36, 18, 9, 41], target: 14. Options for choosing two numbers: [(36, 18), (36, 9), (36, 41), (18, 9), (18, 41), (9, 41)].\n |- Pick two numbers (36, 18) (numbers left: [9, 41]). Try possible operations.\n  |- Try 36 + 18 = 54. Add 54 to the number set. Current number set: [54, 9, 41], target: 14. Options for choosing two numbers: [(54, 9), (54, 41), (9, 41)].\n   |- Pick two numbers (54, 9) (numbers left: [41]). Try possible operations.\n    |- Try 54 + 9 = 63. Add 63 to the number set. Current number set: [63, 41], target: 14, just two numbers left.\n     |- Try 63 + 41 = 104. Evaluate 104 != 14, drop this branch.\n     |- Try 63 - 41 = 22. Evaluate 22 != 14, drop this branch.\n     |- Try 63 * 41 = 2583. 2583 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 54 - 9 = 45. Add 45 to the number set. Current number set: [45, 41], target: 14, just two numbers left.\n     |- Try 45 + 41 = 86. Evaluate 86 != 14, drop this branch.\n     |- Try 45 - 41 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 45 * 41 = 1845. Evaluate 1845 != 14, drop this branch.\n     |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 54 * 9 = 486. Add 486 to the number set. Current number set: [486, 41], target: 14, just two numbers left.\n     |- Try 486 + 41 = 527. Evaluate 527 != 14, drop this branch.\n     |- Try 486 - 41 = 445. Evaluate 445 != 14, drop this branch.\n     |- Try 486 * 41 = 19926. 19926 exceeds the maximum intermediate result, drop this branch.\n     |- Try 486 \/ 41 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 54 \/ 9 = 6. Add 6 to the number set. Current number set: [6, 41], target: 14, just two numbers left.\n     |- Try 41 + 6 = 47. Evaluate 47 != 14, drop this branch.\n     |- Try 41 - 6 = 35. Evaluate 35 != 14, drop this branch.\n     |- Try 41 * 6 = 246. Evaluate 246 != 14, drop this branch.\n     |- Try 41 \/ 6 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (54, 41) (numbers left: [9]). Try possible operations.\n    |- Try 54 + 41 = 95. Add 95 to the number set. Current number set: [95, 9], target: 14, just two numbers left.\n     |- Try 95 + 9 = 104. Evaluate 104 != 14, drop this branch.\n     |- Try 95 - 9 = 86. Evaluate 86 != 14, drop this branch.\n     |- Try 95 * 9 = 855. Evaluate 855 != 14, drop this branch.\n     |- Try 95 \/ 9 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 54 - 41 = 13. Add 13 to the number set. Current number set: [13, 9], target: 14, just two numbers left.\n     |- Try 13 + 9 = 22. Evaluate 22 != 14, drop this branch.\n     |- Try 13 - 9 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 13 * 9 = 117. Evaluate 117 != 14, drop this branch.\n     |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 54 * 41 = 2214. 2214 exceeds the maximum intermediate result, drop this branch.\n    |- Try 54 \/ 41 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (9, 41) (numbers left: [54]). Try possible operations.\n    |- Try 41 + 9 = 50. Add 50 to the number set. Current number set: [50, 54], target: 14, just two numbers left.\n     |- Try 54 + 50 = 104. Evaluate 104 != 14, drop this branch.\n     |- Try 54 - 50 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 54 * 50 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 50 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 - 9 = 32. Add 32 to the number set. Current number set: [32, 54], target: 14, just two numbers left.\n     |- Try 54 + 32 = 86. Evaluate 86 != 14, drop this branch.\n     |- Try 54 - 32 = 22. Evaluate 22 != 14, drop this branch.\n     |- Try 54 * 32 = 1728. Evaluate 1728 != 14, drop this branch.\n     |- Try 54 \/ 32 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 41 * 9 = 369. Add 369 to the number set. Current number set: [369, 54], target: 14, just two numbers left.\n     |- Try 369 + 54 = 423. Evaluate 423 != 14, drop this branch.\n     |- Try 369 - 54 = 315. Evaluate 315 != 14, drop this branch.\n     |- Try 369 * 54 = 19926. 19926 exceeds the maximum intermediate result, drop this branch.\n     |- Try 369 \/ 54 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 36 - 18 = 18. Add 18 to the number set. Current number set: [18, 9, 41], target: 14. Options for choosing two numbers: [(18, 9), (18, 41), (9, 41)].\n   |- Pick two numbers (18, 9) (numbers left: [41]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 41], target: 14, just two numbers left.\n     |- Try 41 + 27 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 41 - 27 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 - 27 = 14\nThe step before: 18 + 9 = 27\nThe first step: 36 - 18 = 18\n\nOutput the solution in the required format:\n<Solution>\n36 - 18 = 18\n18 + 9 = 27\n41 - 27 = 14\n<\/Solution>\n","item":{"nums":[36,18,9,41],"solution":["36 - 18 = 18","18 + 9 = 27","41 - 27 = 14"],"target":14}}
+{"instance_id":"countdown_2k_22","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 8, 18, 29]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [30, 8, 18, 29], target: 25. Options for choosing two numbers: [(30, 8), (30, 18), (30, 29), (8, 18), (8, 29), (18, 29)].\n |- Pick two numbers (30, 8) (numbers left: [18, 29]). Try possible operations.\n  |- Try 30 + 8 = 38. Add 38 to the number set. Current number set: [38, 18, 29], target: 25. Options for choosing two numbers: [(38, 18), (38, 29), (18, 29)].\n   |- Pick two numbers (38, 18) (numbers left: [29]). Try possible operations.\n    |- Try 38 + 18 = 56. Add 56 to the number set. Current number set: [56, 29], target: 25, just two numbers left.\n     |- Try 56 + 29 = 85. Evaluate 85 != 25, drop this branch.\n     |- Try 56 - 29 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 56 * 29 = 1624. Evaluate 1624 != 25, drop this branch.\n     |- Try 56 \/ 29 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 38 - 18 = 20. Add 20 to the number set. Current number set: [20, 29], target: 25, just two numbers left.\n     |- Try 29 + 20 = 49. Evaluate 49 != 25, drop this branch.\n     |- Try 29 - 20 = 9. Evaluate 9 != 25, drop this branch.\n     |- Try 29 * 20 = 580. Evaluate 580 != 25, drop this branch.\n     |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 38 * 18 = 684. Add 684 to the number set. Current number set: [684, 29], target: 25, just two numbers left.\n     |- Try 684 + 29 = 713. Evaluate 713 != 25, drop this branch.\n     |- Try 684 - 29 = 655. Evaluate 655 != 25, drop this branch.\n     |- Try 684 * 29 = 19836. 19836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 29 = 23.6. 23.6 is a decimal, drop this branch.\n    |- Try 38 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (38, 29) (numbers left: [18]). Try possible operations.\n    |- Try 38 + 29 = 67. Add 67 to the number set. Current number set: [67, 18], target: 25, just two numbers left.\n     |- Try 67 + 18 = 85. Evaluate 85 != 25, drop this branch.\n     |- Try 67 - 18 = 49. Evaluate 49 != 25, drop this branch.\n     |- Try 67 * 18 = 1206. Evaluate 1206 != 25, drop this branch.\n     |- Try 67 \/ 18 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 38 - 29 = 9. Add 9 to the number set. Current number set: [9, 18], target: 25, just two numbers left.\n     |- Try 18 + 9 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 18 - 9 = 9. Evaluate 9 != 25, drop this branch.\n     |- Try 18 * 9 = 162. Evaluate 162 != 25, drop this branch.\n     |- Try 18 \/ 9 = 2. Evaluate 2 != 25, drop this branch.\n    |- Try 38 * 29 = 1102. Add 1102 to the number set. Current number set: [1102, 18], target: 25, just two numbers left.\n     |- Try 1102 + 18 = 1120. Evaluate 1120 != 25, drop this branch.\n     |- Try 1102 - 18 = 1084. Evaluate 1084 != 25, drop this branch.\n     |- Try 1102 * 18 = 19836. 19836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1102 \/ 18 = 61.2. 61.2 is a decimal, drop this branch.\n    |- Try 38 \/ 29 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (18, 29) (numbers left: [38]). Try possible operations.\n    |- Try 29 + 18 = 47. Add 47 to the number set. Current number set: [47, 38], target: 25, just two numbers left.\n     |- Try 47 + 38 = 85. Evaluate 85 != 25, drop this branch.\n     |- Try 47 - 38 = 9. Evaluate 9 != 25, drop this branch.\n     |- Try 47 * 38 = 1786. Evaluate 1786 != 25, drop this branch.\n     |- Try 47 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 29 - 18 = 11. Add 11 to the number set. Current number set: [11, 38], target: 25, just two numbers left.\n     |- Try 38 + 11 = 49. Evaluate 49 != 25, drop this branch.\n     |- Try 38 - 11 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 38 * 11 = 418. Evaluate 418 != 25, drop this branch.\n     |- Try 38 \/ 11 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 29 * 18 = 522. Add 522 to the number set. Current number set: [522, 38], target: 25, just two numbers left.\n     |- Try 522 + 38 = 560. Evaluate 560 != 25, drop this branch.\n     |- Try 522 - 38 = 484. Evaluate 484 != 25, drop this branch.\n     |- Try 522 * 38 = 19836. 19836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 522 \/ 38 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 29 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 30 - 8 = 22. Add 22 to the number set. Current number set: [22, 18, 29], target: 25. Options for choosing two numbers: [(22, 18), (22, 29), (18, 29)].\n   |- Pick two numbers (22, 18) (numbers left: [29]). Try possible operations.\n    |- Try 22 + 18 = 40. Add 40 to the number set. Current number set: [40, 29], target: 25, just two numbers left.\n     |- Try 40 + 29 = 69. Evaluate 69 != 25, drop this branch.\n     |- Try 40 - 29 = 11. Evaluate 11 != 25, drop this branch.\n     |- Try 40 * 29 = 1160. Evaluate 1160 != 25, drop this branch.\n     |- Try 40 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 - 18 = 4. Add 4 to the number set. Current number set: [4, 29], target: 25, just two numbers left.\n     |- Try 29 + 4 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 29 - 4 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 - 4 = 25\nThe step before: 22 - 18 = 4\nThe first step: 30 - 8 = 22\n\nOutput the solution in the required format:\n<Solution>\n30 - 8 = 22\n22 - 18 = 4\n29 - 4 = 25\n<\/Solution>\n","item":{"nums":[30,8,18,29],"solution":["30 - 8 = 22","22 - 18 = 4","29 - 4 = 25"],"target":25}}
+{"instance_id":"countdown_2k_23","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 44, 16, 3]\nTarget: 47","reference_output":"# Search Procedure\nInitial number set: [10, 44, 16, 3], target: 47. Options for choosing two numbers: [(10, 44), (10, 16), (10, 3), (44, 16), (44, 3), (16, 3)].\n |- Pick two numbers (10, 44) (numbers left: [16, 3]). Try possible operations.\n  |- Try 44 + 10 = 54. Add 54 to the number set. Current number set: [54, 16, 3], target: 47. Options for choosing two numbers: [(54, 16), (54, 3), (16, 3)].\n   |- Pick two numbers (54, 16) (numbers left: [3]). Try possible operations.\n    |- Try 54 + 16 = 70. Add 70 to the number set. Current number set: [70, 3], target: 47, just two numbers left.\n     |- Try 70 + 3 = 73. Evaluate 73 != 47, drop this branch.\n     |- Try 70 - 3 = 67. Evaluate 67 != 47, drop this branch.\n     |- Try 70 * 3 = 210. Evaluate 210 != 47, drop this branch.\n     |- Try 70 \/ 3 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 54 - 16 = 38. Add 38 to the number set. Current number set: [38, 3], target: 47, just two numbers left.\n     |- Try 38 + 3 = 41. Evaluate 41 != 47, drop this branch.\n     |- Try 38 - 3 = 35. Evaluate 35 != 47, drop this branch.\n     |- Try 38 * 3 = 114. Evaluate 114 != 47, drop this branch.\n     |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 54 * 16 = 864. Add 864 to the number set. Current number set: [864, 3], target: 47, just two numbers left.\n     |- Try 864 + 3 = 867. Evaluate 867 != 47, drop this branch.\n     |- Try 864 - 3 = 861. Evaluate 861 != 47, drop this branch.\n     |- Try 864 * 3 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 3 = 288. Evaluate 288 != 47, drop this branch.\n    |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (54, 3) (numbers left: [16]). Try possible operations.\n    |- Try 54 + 3 = 57. Add 57 to the number set. Current number set: [57, 16], target: 47, just two numbers left.\n     |- Try 57 + 16 = 73. Evaluate 73 != 47, drop this branch.\n     |- Try 57 - 16 = 41. Evaluate 41 != 47, drop this branch.\n     |- Try 57 * 16 = 912. Evaluate 912 != 47, drop this branch.\n     |- Try 57 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 54 - 3 = 51. Add 51 to the number set. Current number set: [51, 16], target: 47, just two numbers left.\n     |- Try 51 + 16 = 67. Evaluate 67 != 47, drop this branch.\n     |- Try 51 - 16 = 35. Evaluate 35 != 47, drop this branch.\n     |- Try 51 * 16 = 816. Evaluate 816 != 47, drop this branch.\n     |- Try 51 \/ 16 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 54 * 3 = 162. Add 162 to the number set. Current number set: [162, 16], target: 47, just two numbers left.\n     |- Try 162 + 16 = 178. Evaluate 178 != 47, drop this branch.\n     |- Try 162 - 16 = 146. Evaluate 146 != 47, drop this branch.\n     |- Try 162 * 16 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 16 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 54 \/ 3 = 18. Add 18 to the number set. Current number set: [18, 16], target: 47, just two numbers left.\n     |- Try 18 + 16 = 34. Evaluate 34 != 47, drop this branch.\n     |- Try 18 - 16 = 2. Evaluate 2 != 47, drop this branch.\n     |- Try 18 * 16 = 288. Evaluate 288 != 47, drop this branch.\n     |- Try 18 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (16, 3) (numbers left: [54]). Try possible operations.\n    |- Try 16 + 3 = 19. Add 19 to the number set. Current number set: [19, 54], target: 47, just two numbers left.\n     |- Try 54 + 19 = 73. Evaluate 73 != 47, drop this branch.\n     |- Try 54 - 19 = 35. Evaluate 35 != 47, drop this branch.\n     |- Try 54 * 19 = 1026. Evaluate 1026 != 47, drop this branch.\n     |- Try 54 \/ 19 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 16 - 3 = 13. Add 13 to the number set. Current number set: [13, 54], target: 47, just two numbers left.\n     |- Try 54 + 13 = 67. Evaluate 67 != 47, drop this branch.\n     |- Try 54 - 13 = 41. Evaluate 41 != 47, drop this branch.\n     |- Try 54 * 13 = 702. Evaluate 702 != 47, drop this branch.\n     |- Try 54 \/ 13 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 16 * 3 = 48. Add 48 to the number set. Current number set: [48, 54], target: 47, just two numbers left.\n     |- Try 54 + 48 = 102. Evaluate 102 != 47, drop this branch.\n     |- Try 54 - 48 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 54 * 48 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 48 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n  |- Try 44 - 10 = 34. Add 34 to the number set. Current number set: [34, 16, 3], target: 47. Options for choosing two numbers: [(34, 16), (34, 3), (16, 3)].\n   |- Pick two numbers (34, 16) (numbers left: [3]). Try possible operations.\n    |- Try 34 + 16 = 50. Add 50 to the number set. Current number set: [50, 3], target: 47, just two numbers left.\n     |- Try 50 + 3 = 53. Evaluate 53 != 47, drop this branch.\n     |- Try 50 - 3 = 47. Evaluate 47 == 47, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 50 - 3 = 47\nThe step before: 34 + 16 = 50\nThe first step: 44 - 10 = 34\n\nOutput the solution in the required format:\n<Solution>\n44 - 10 = 34\n34 + 16 = 50\n50 - 3 = 47\n<\/Solution>\n","item":{"nums":[10,44,16,3],"solution":["44 - 10 = 34","34 + 16 = 50","50 - 3 = 47"],"target":47}}
+{"instance_id":"countdown_2k_24","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 42, 4, 6]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [19, 42, 4, 6], target: 25. Options for choosing two numbers: [(19, 42), (19, 4), (19, 6), (42, 4), (42, 6), (4, 6)].\n |- Pick two numbers (19, 42) (numbers left: [4, 6]). Try possible operations.\n  |- Try 42 + 19 = 61. Add 61 to the number set. Current number set: [61, 4, 6], target: 25. Options for choosing two numbers: [(61, 4), (61, 6), (4, 6)].\n   |- Pick two numbers (61, 4) (numbers left: [6]). Try possible operations.\n    |- Try 61 + 4 = 65. Add 65 to the number set. Current number set: [65, 6], target: 25, just two numbers left.\n     |- Try 65 + 6 = 71. Evaluate 71 != 25, drop this branch.\n     |- Try 65 - 6 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 65 * 6 = 390. Evaluate 390 != 25, drop this branch.\n     |- Try 65 \/ 6 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 61 - 4 = 57. Add 57 to the number set. Current number set: [57, 6], target: 25, just two numbers left.\n     |- Try 57 + 6 = 63. Evaluate 63 != 25, drop this branch.\n     |- Try 57 - 6 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 57 * 6 = 342. Evaluate 342 != 25, drop this branch.\n     |- Try 57 \/ 6 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 61 * 4 = 244. Add 244 to the number set. Current number set: [244, 6], target: 25, just two numbers left.\n     |- Try 244 + 6 = 250. Evaluate 250 != 25, drop this branch.\n     |- Try 244 - 6 = 238. Evaluate 238 != 25, drop this branch.\n     |- Try 244 * 6 = 1464. Evaluate 1464 != 25, drop this branch.\n     |- Try 244 \/ 6 = 40.7. 40.7 is a decimal, drop this branch.\n    |- Try 61 \/ 4 = 15.2. 15.2 is a decimal, drop this branch.\n   |- Pick two numbers (61, 6) (numbers left: [4]). Try possible operations.\n    |- Try 61 + 6 = 67. Add 67 to the number set. Current number set: [67, 4], target: 25, just two numbers left.\n     |- Try 67 + 4 = 71. Evaluate 71 != 25, drop this branch.\n     |- Try 67 - 4 = 63. Evaluate 63 != 25, drop this branch.\n     |- Try 67 * 4 = 268. Evaluate 268 != 25, drop this branch.\n     |- Try 67 \/ 4 = 16.8. 16.8 is a decimal, drop this branch.\n    |- Try 61 - 6 = 55. Add 55 to the number set. Current number set: [55, 4], target: 25, just two numbers left.\n     |- Try 55 + 4 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 55 - 4 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 55 * 4 = 220. Evaluate 220 != 25, drop this branch.\n     |- Try 55 \/ 4 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 61 * 6 = 366. Add 366 to the number set. Current number set: [366, 4], target: 25, just two numbers left.\n     |- Try 366 + 4 = 370. Evaluate 370 != 25, drop this branch.\n     |- Try 366 - 4 = 362. Evaluate 362 != 25, drop this branch.\n     |- Try 366 * 4 = 1464. Evaluate 1464 != 25, drop this branch.\n     |- Try 366 \/ 4 = 91.5. 91.5 is a decimal, drop this branch.\n    |- Try 61 \/ 6 = 10.2. 10.2 is a decimal, drop this branch.\n   |- Pick two numbers (4, 6) (numbers left: [61]). Try possible operations.\n    |- Try 6 + 4 = 10. Add 10 to the number set. Current number set: [10, 61], target: 25, just two numbers left.\n     |- Try 61 + 10 = 71. Evaluate 71 != 25, drop this branch.\n     |- Try 61 - 10 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 61 * 10 = 610. Evaluate 610 != 25, drop this branch.\n     |- Try 61 \/ 10 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 6 - 4 = 2. Add 2 to the number set. Current number set: [2, 61], target: 25, just two numbers left.\n     |- Try 61 + 2 = 63. Evaluate 63 != 25, drop this branch.\n     |- Try 61 - 2 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 61 * 2 = 122. Evaluate 122 != 25, drop this branch.\n     |- Try 61 \/ 2 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 6 * 4 = 24. Add 24 to the number set. Current number set: [24, 61], target: 25, just two numbers left.\n     |- Try 61 + 24 = 85. Evaluate 85 != 25, drop this branch.\n     |- Try 61 - 24 = 37. Evaluate 37 != 25, drop this branch.\n     |- Try 61 * 24 = 1464. Evaluate 1464 != 25, drop this branch.\n     |- Try 61 \/ 24 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 42 - 19 = 23. Add 23 to the number set. Current number set: [23, 4, 6], target: 25. Options for choosing two numbers: [(23, 4), (23, 6), (4, 6)].\n   |- Pick two numbers (23, 4) (numbers left: [6]). Try possible operations.\n    |- Try 23 + 4 = 27. Add 27 to the number set. Current number set: [27, 6], target: 25, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 25, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 25, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 23 - 4 = 19. Add 19 to the number set. Current number set: [19, 6], target: 25, just two numbers left.\n     |- Try 19 + 6 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 + 6 = 25\nThe step before: 23 - 4 = 19\nThe first step: 42 - 19 = 23\n\nOutput the solution in the required format:\n<Solution>\n42 - 19 = 23\n23 - 4 = 19\n19 + 6 = 25\n<\/Solution>\n","item":{"nums":[19,42,4,6],"solution":["42 - 19 = 23","23 - 4 = 19","19 + 6 = 25"],"target":25}}
+{"instance_id":"countdown_2k_25","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 19, 24, 40]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [41, 19, 24, 40], target: 16. Options for choosing two numbers: [(41, 19), (41, 24), (41, 40), (19, 24), (19, 40), (24, 40)].\n |- Pick two numbers (41, 19) (numbers left: [24, 40]). Try possible operations.\n  |- Try 41 + 19 = 60. Add 60 to the number set. Current number set: [60, 24, 40], target: 16. Options for choosing two numbers: [(60, 24), (60, 40), (24, 40)].\n   |- Pick two numbers (60, 24) (numbers left: [40]). Try possible operations.\n    |- Try 60 + 24 = 84. Add 84 to the number set. Current number set: [84, 40], target: 16, just two numbers left.\n     |- Try 84 + 40 = 124. Evaluate 124 != 16, drop this branch.\n     |- Try 84 - 40 = 44. Evaluate 44 != 16, drop this branch.\n     |- Try 84 * 40 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 40 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 60 - 24 = 36. Add 36 to the number set. Current number set: [36, 40], target: 16, just two numbers left.\n     |- Try 40 + 36 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 40 - 36 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 40 * 36 = 1440. Evaluate 1440 != 16, drop this branch.\n     |- Try 40 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 60 * 24 = 1440. Add 1440 to the number set. Current number set: [1440, 40], target: 16, just two numbers left.\n     |- Try 1440 + 40 = 1480. Evaluate 1480 != 16, drop this branch.\n     |- Try 1440 - 40 = 1400. Evaluate 1400 != 16, drop this branch.\n     |- Try 1440 * 40 = 57600. 57600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1440 \/ 40 = 36. Evaluate 36 != 16, drop this branch.\n    |- Try 60 \/ 24 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (60, 40) (numbers left: [24]). Try possible operations.\n    |- Try 60 + 40 = 100. Add 100 to the number set. Current number set: [100, 24], target: 16, just two numbers left.\n     |- Try 100 + 24 = 124. Evaluate 124 != 16, drop this branch.\n     |- Try 100 - 24 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 100 * 24 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 24 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 60 - 40 = 20. Add 20 to the number set. Current number set: [20, 24], target: 16, just two numbers left.\n     |- Try 24 + 20 = 44. Evaluate 44 != 16, drop this branch.\n     |- Try 24 - 20 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 24 * 20 = 480. Evaluate 480 != 16, drop this branch.\n     |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 60 * 40 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 40 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 40) (numbers left: [60]). Try possible operations.\n    |- Try 40 + 24 = 64. Add 64 to the number set. Current number set: [64, 60], target: 16, just two numbers left.\n     |- Try 64 + 60 = 124. Evaluate 124 != 16, drop this branch.\n     |- Try 64 - 60 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 64 * 60 = 3840. 3840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 60 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 - 24 = 16. Add 16 to the number set. Current number set: [16, 60], target: 16, just two numbers left.\n     |- Try 60 + 16 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 60 - 16 = 44. Evaluate 44 != 16, drop this branch.\n     |- Try 60 * 16 = 960. Evaluate 960 != 16, drop this branch.\n     |- Try 60 \/ 16 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 40 * 24 = 960. Add 960 to the number set. Current number set: [960, 60], target: 16, just two numbers left.\n     |- Try 960 + 60 = 1020. Evaluate 1020 != 16, drop this branch.\n     |- Try 960 - 60 = 900. Evaluate 900 != 16, drop this branch.\n     |- Try 960 * 60 = 57600. 57600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 60 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 960 \/ 60 = 16\nThe step before: 40 * 24 = 960\nThe first step: 41 + 19 = 60\n\nOutput the solution in the required format:\n<Solution>\n41 + 19 = 60\n40 * 24 = 960\n960 \/ 60 = 16\n<\/Solution>\n","item":{"nums":[41,19,24,40],"solution":["41 + 19 = 60","40 * 24 = 960","960 \/ 60 = 16"],"target":16}}
+{"instance_id":"countdown_2k_26","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 4, 36, 30]\nTarget: 39","reference_output":"# Search Procedure\nInitial number set: [37, 4, 36, 30], target: 39. Options for choosing two numbers: [(37, 4), (37, 36), (37, 30), (4, 36), (4, 30), (36, 30)].\n |- Pick two numbers (37, 4) (numbers left: [36, 30]). Try possible operations.\n  |- Try 37 + 4 = 41. Add 41 to the number set. Current number set: [41, 36, 30], target: 39. Options for choosing two numbers: [(41, 36), (41, 30), (36, 30)].\n   |- Pick two numbers (41, 36) (numbers left: [30]). Try possible operations.\n    |- Try 41 + 36 = 77. Add 77 to the number set. Current number set: [77, 30], target: 39, just two numbers left.\n     |- Try 77 + 30 = 107. Evaluate 107 != 39, drop this branch.\n     |- Try 77 - 30 = 47. Evaluate 47 != 39, drop this branch.\n     |- Try 77 * 30 = 2310. 2310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 41 - 36 = 5. Add 5 to the number set. Current number set: [5, 30], target: 39, just two numbers left.\n     |- Try 30 + 5 = 35. Evaluate 35 != 39, drop this branch.\n     |- Try 30 - 5 = 25. Evaluate 25 != 39, drop this branch.\n     |- Try 30 * 5 = 150. Evaluate 150 != 39, drop this branch.\n     |- Try 30 \/ 5 = 6. Evaluate 6 != 39, drop this branch.\n    |- Try 41 * 36 = 1476. Add 1476 to the number set. Current number set: [1476, 30], target: 39, just two numbers left.\n     |- Try 1476 + 30 = 1506. Evaluate 1506 != 39, drop this branch.\n     |- Try 1476 - 30 = 1446. Evaluate 1446 != 39, drop this branch.\n     |- Try 1476 * 30 = 44280. 44280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1476 \/ 30 = 49.2. 49.2 is a decimal, drop this branch.\n    |- Try 41 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (41, 30) (numbers left: [36]). Try possible operations.\n    |- Try 41 + 30 = 71. Add 71 to the number set. Current number set: [71, 36], target: 39, just two numbers left.\n     |- Try 71 + 36 = 107. Evaluate 107 != 39, drop this branch.\n     |- Try 71 - 36 = 35. Evaluate 35 != 39, drop this branch.\n     |- Try 71 * 36 = 2556. 2556 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 36 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 41 - 30 = 11. Add 11 to the number set. Current number set: [11, 36], target: 39, just two numbers left.\n     |- Try 36 + 11 = 47. Evaluate 47 != 39, drop this branch.\n     |- Try 36 - 11 = 25. Evaluate 25 != 39, drop this branch.\n     |- Try 36 * 11 = 396. Evaluate 396 != 39, drop this branch.\n     |- Try 36 \/ 11 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 41 * 30 = 1230. Add 1230 to the number set. Current number set: [1230, 36], target: 39, just two numbers left.\n     |- Try 1230 + 36 = 1266. Evaluate 1266 != 39, drop this branch.\n     |- Try 1230 - 36 = 1194. Evaluate 1194 != 39, drop this branch.\n     |- Try 1230 * 36 = 44280. 44280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 36 = 34.2. 34.2 is a decimal, drop this branch.\n    |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (36, 30) (numbers left: [41]). Try possible operations.\n    |- Try 36 + 30 = 66. Add 66 to the number set. Current number set: [66, 41], target: 39, just two numbers left.\n     |- Try 66 + 41 = 107. Evaluate 107 != 39, drop this branch.\n     |- Try 66 - 41 = 25. Evaluate 25 != 39, drop this branch.\n     |- Try 66 * 41 = 2706. 2706 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 41 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 - 30 = 6. Add 6 to the number set. Current number set: [6, 41], target: 39, just two numbers left.\n     |- Try 41 + 6 = 47. Evaluate 47 != 39, drop this branch.\n     |- Try 41 - 6 = 35. Evaluate 35 != 39, drop this branch.\n     |- Try 41 * 6 = 246. Evaluate 246 != 39, drop this branch.\n     |- Try 41 \/ 6 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 36 * 30 = 1080. Add 1080 to the number set. Current number set: [1080, 41], target: 39, just two numbers left.\n     |- Try 1080 + 41 = 1121. Evaluate 1121 != 39, drop this branch.\n     |- Try 1080 - 41 = 1039. Evaluate 1039 != 39, drop this branch.\n     |- Try 1080 * 41 = 44280. 44280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 41 = 26.3. 26.3 is a decimal, drop this branch.\n    |- Try 36 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 37 - 4 = 33. Add 33 to the number set. Current number set: [33, 36, 30], target: 39. Options for choosing two numbers: [(33, 36), (33, 30), (36, 30)].\n   |- Pick two numbers (33, 36) (numbers left: [30]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 30], target: 39, just two numbers left.\n     |- Try 69 + 30 = 99. Evaluate 99 != 39, drop this branch.\n     |- Try 69 - 30 = 39. Evaluate 39 == 39, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 69 - 30 = 39\nThe step before: 36 + 33 = 69\nThe first step: 37 - 4 = 33\n\nOutput the solution in the required format:\n<Solution>\n37 - 4 = 33\n36 + 33 = 69\n69 - 30 = 39\n<\/Solution>\n","item":{"nums":[37,4,36,30],"solution":["37 - 4 = 33","36 + 33 = 69","69 - 30 = 39"],"target":39}}
+{"instance_id":"countdown_2k_27","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [25, 6, 44, 43]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [25, 6, 44, 43], target: 18. Options for choosing two numbers: [(25, 6), (25, 44), (25, 43), (6, 44), (6, 43), (44, 43)].\n |- Pick two numbers (25, 6) (numbers left: [44, 43]). Try possible operations.\n  |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 44, 43], target: 18. Options for choosing two numbers: [(31, 44), (31, 43), (44, 43)].\n   |- Pick two numbers (31, 44) (numbers left: [43]). Try possible operations.\n    |- Try 44 + 31 = 75. Add 75 to the number set. Current number set: [75, 43], target: 18, just two numbers left.\n     |- Try 75 + 43 = 118. Evaluate 118 != 18, drop this branch.\n     |- Try 75 - 43 = 32. Evaluate 32 != 18, drop this branch.\n     |- Try 75 * 43 = 3225. 3225 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 43 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 44 - 31 = 13. Add 13 to the number set. Current number set: [13, 43], target: 18, just two numbers left.\n     |- Try 43 + 13 = 56. Evaluate 56 != 18, drop this branch.\n     |- Try 43 - 13 = 30. Evaluate 30 != 18, drop this branch.\n     |- Try 43 * 13 = 559. Evaluate 559 != 18, drop this branch.\n     |- Try 43 \/ 13 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 44 * 31 = 1364. Add 1364 to the number set. Current number set: [1364, 43], target: 18, just two numbers left.\n     |- Try 1364 + 43 = 1407. Evaluate 1407 != 18, drop this branch.\n     |- Try 1364 - 43 = 1321. Evaluate 1321 != 18, drop this branch.\n     |- Try 1364 * 43 = 58652. 58652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1364 \/ 43 = 31.7. 31.7 is a decimal, drop this branch.\n    |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (31, 43) (numbers left: [44]). Try possible operations.\n    |- Try 43 + 31 = 74. Add 74 to the number set. Current number set: [74, 44], target: 18, just two numbers left.\n     |- Try 74 + 44 = 118. Evaluate 118 != 18, drop this branch.\n     |- Try 74 - 44 = 30. Evaluate 30 != 18, drop this branch.\n     |- Try 74 * 44 = 3256. 3256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 44 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 43 - 31 = 12. Add 12 to the number set. Current number set: [12, 44], target: 18, just two numbers left.\n     |- Try 44 + 12 = 56. Evaluate 56 != 18, drop this branch.\n     |- Try 44 - 12 = 32. Evaluate 32 != 18, drop this branch.\n     |- Try 44 * 12 = 528. Evaluate 528 != 18, drop this branch.\n     |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 43 * 31 = 1333. Add 1333 to the number set. Current number set: [1333, 44], target: 18, just two numbers left.\n     |- Try 1333 + 44 = 1377. Evaluate 1377 != 18, drop this branch.\n     |- Try 1333 - 44 = 1289. Evaluate 1289 != 18, drop this branch.\n     |- Try 1333 * 44 = 58652. 58652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1333 \/ 44 = 30.3. 30.3 is a decimal, drop this branch.\n    |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (44, 43) (numbers left: [31]). Try possible operations.\n    |- Try 44 + 43 = 87. Add 87 to the number set. Current number set: [87, 31], target: 18, just two numbers left.\n     |- Try 87 + 31 = 118. Evaluate 118 != 18, drop this branch.\n     |- Try 87 - 31 = 56. Evaluate 56 != 18, drop this branch.\n     |- Try 87 * 31 = 2697. 2697 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 31 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 44 - 43 = 1. Add 1 to the number set. Current number set: [1, 31], target: 18, just two numbers left.\n     |- Try 31 + 1 = 32. Evaluate 32 != 18, drop this branch.\n     |- Try 31 - 1 = 30. Evaluate 30 != 18, drop this branch.\n     |- Try 31 * 1 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 31 \/ 1 = 31. Evaluate 31 != 18, drop this branch.\n    |- Try 44 * 43 = 1892. Add 1892 to the number set. Current number set: [1892, 31], target: 18, just two numbers left.\n     |- Try 1892 + 31 = 1923. Evaluate 1923 != 18, drop this branch.\n     |- Try 1892 - 31 = 1861. Evaluate 1861 != 18, drop this branch.\n     |- Try 1892 * 31 = 58652. 58652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1892 \/ 31 = 61.0. 61.0 is a decimal, drop this branch.\n    |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 44, 43], target: 18. Options for choosing two numbers: [(19, 44), (19, 43), (44, 43)].\n   |- Pick two numbers (19, 44) (numbers left: [43]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 43], target: 18, just two numbers left.\n     |- Try 63 + 43 = 106. Evaluate 106 != 18, drop this branch.\n     |- Try 63 - 43 = 20. Evaluate 20 != 18, drop this branch.\n     |- Try 63 * 43 = 2709. 2709 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 43 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 43], target: 18, just two numbers left.\n     |- Try 43 + 25 = 68. Evaluate 68 != 18, drop this branch.\n     |- Try 43 - 25 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 - 25 = 18\nThe step before: 44 - 19 = 25\nThe first step: 25 - 6 = 19\n\nOutput the solution in the required format:\n<Solution>\n25 - 6 = 19\n44 - 19 = 25\n43 - 25 = 18\n<\/Solution>\n","item":{"nums":[25,6,44,43],"solution":["25 - 6 = 19","44 - 19 = 25","43 - 25 = 18"],"target":18}}
+{"instance_id":"countdown_2k_28","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 41, 44, 28]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [12, 41, 44, 28], target: 13. Options for choosing two numbers: [(12, 41), (12, 44), (12, 28), (41, 44), (41, 28), (44, 28)].\n |- Pick two numbers (12, 41) (numbers left: [44, 28]). Try possible operations.\n  |- Try 41 + 12 = 53. Add 53 to the number set. Current number set: [53, 44, 28], target: 13. Options for choosing two numbers: [(53, 44), (53, 28), (44, 28)].\n   |- Pick two numbers (53, 44) (numbers left: [28]). Try possible operations.\n    |- Try 53 + 44 = 97. Add 97 to the number set. Current number set: [97, 28], target: 13, just two numbers left.\n     |- Try 97 + 28 = 125. Evaluate 125 != 13, drop this branch.\n     |- Try 97 - 28 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 97 * 28 = 2716. 2716 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 28 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 53 - 44 = 9. Add 9 to the number set. Current number set: [9, 28], target: 13, just two numbers left.\n     |- Try 28 + 9 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 28 - 9 = 19. Evaluate 19 != 13, drop this branch.\n     |- Try 28 * 9 = 252. Evaluate 252 != 13, drop this branch.\n     |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 53 * 44 = 2332. 2332 exceeds the maximum intermediate result, drop this branch.\n    |- Try 53 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (53, 28) (numbers left: [44]). Try possible operations.\n    |- Try 53 + 28 = 81. Add 81 to the number set. Current number set: [81, 44], target: 13, just two numbers left.\n     |- Try 81 + 44 = 125. Evaluate 125 != 13, drop this branch.\n     |- Try 81 - 44 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 81 * 44 = 3564. 3564 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 44 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 53 - 28 = 25. Add 25 to the number set. Current number set: [25, 44], target: 13, just two numbers left.\n     |- Try 44 + 25 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 44 - 25 = 19. Evaluate 19 != 13, drop this branch.\n     |- Try 44 * 25 = 1100. Evaluate 1100 != 13, drop this branch.\n     |- Try 44 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 53 * 28 = 1484. Add 1484 to the number set. Current number set: [1484, 44], target: 13, just two numbers left.\n     |- Try 1484 + 44 = 1528. Evaluate 1528 != 13, drop this branch.\n     |- Try 1484 - 44 = 1440. Evaluate 1440 != 13, drop this branch.\n     |- Try 1484 * 44 = 65296. 65296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1484 \/ 44 = 33.7. 33.7 is a decimal, drop this branch.\n    |- Try 53 \/ 28 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 28) (numbers left: [53]). Try possible operations.\n    |- Try 44 + 28 = 72. Add 72 to the number set. Current number set: [72, 53], target: 13, just two numbers left.\n     |- Try 72 + 53 = 125. Evaluate 125 != 13, drop this branch.\n     |- Try 72 - 53 = 19. Evaluate 19 != 13, drop this branch.\n     |- Try 72 * 53 = 3816. 3816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 53 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 28 = 16. Add 16 to the number set. Current number set: [16, 53], target: 13, just two numbers left.\n     |- Try 53 + 16 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 53 - 16 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 53 * 16 = 848. Evaluate 848 != 13, drop this branch.\n     |- Try 53 \/ 16 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 44 * 28 = 1232. Add 1232 to the number set. Current number set: [1232, 53], target: 13, just two numbers left.\n     |- Try 1232 + 53 = 1285. Evaluate 1285 != 13, drop this branch.\n     |- Try 1232 - 53 = 1179. Evaluate 1179 != 13, drop this branch.\n     |- Try 1232 * 53 = 65296. 65296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1232 \/ 53 = 23.2. 23.2 is a decimal, drop this branch.\n    |- Try 44 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 41 - 12 = 29. Add 29 to the number set. Current number set: [29, 44, 28], target: 13. Options for choosing two numbers: [(29, 44), (29, 28), (44, 28)].\n   |- Pick two numbers (29, 44) (numbers left: [28]). Try possible operations.\n    |- Try 44 + 29 = 73. Add 73 to the number set. Current number set: [73, 28], target: 13, just two numbers left.\n     |- Try 73 + 28 = 101. Evaluate 101 != 13, drop this branch.\n     |- Try 73 - 28 = 45. Evaluate 45 != 13, drop this branch.\n     |- Try 73 * 28 = 2044. 2044 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 28 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 44 - 29 = 15. Add 15 to the number set. Current number set: [15, 28], target: 13, just two numbers left.\n     |- Try 28 + 15 = 43. Evaluate 43 != 13, drop this branch.\n     |- Try 28 - 15 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 - 15 = 13\nThe step before: 44 - 29 = 15\nThe first step: 41 - 12 = 29\n\nOutput the solution in the required format:\n<Solution>\n41 - 12 = 29\n44 - 29 = 15\n28 - 15 = 13\n<\/Solution>\n","item":{"nums":[12,41,44,28],"solution":["41 - 12 = 29","44 - 29 = 15","28 - 15 = 13"],"target":13}}
+{"instance_id":"countdown_2k_29","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 6, 29, 24]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [42, 6, 29, 24], target: 31. Options for choosing two numbers: [(42, 6), (42, 29), (42, 24), (6, 29), (6, 24), (29, 24)].\n |- Pick two numbers (42, 6) (numbers left: [29, 24]). Try possible operations.\n  |- Try 42 + 6 = 48. Add 48 to the number set. Current number set: [48, 29, 24], target: 31. Options for choosing two numbers: [(48, 29), (48, 24), (29, 24)].\n   |- Pick two numbers (48, 29) (numbers left: [24]). Try possible operations.\n    |- Try 48 + 29 = 77. Add 77 to the number set. Current number set: [77, 24], target: 31, just two numbers left.\n     |- Try 77 + 24 = 101. Evaluate 101 != 31, drop this branch.\n     |- Try 77 - 24 = 53. Evaluate 53 != 31, drop this branch.\n     |- Try 77 * 24 = 1848. Evaluate 1848 != 31, drop this branch.\n     |- Try 77 \/ 24 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 48 - 29 = 19. Add 19 to the number set. Current number set: [19, 24], target: 31, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 31, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 31, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 31, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 * 29 = 1392. Add 1392 to the number set. Current number set: [1392, 24], target: 31, just two numbers left.\n     |- Try 1392 + 24 = 1416. Evaluate 1416 != 31, drop this branch.\n     |- Try 1392 - 24 = 1368. Evaluate 1368 != 31, drop this branch.\n     |- Try 1392 * 24 = 33408. 33408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1392 \/ 24 = 58. Evaluate 58 != 31, drop this branch.\n    |- Try 48 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (48, 24) (numbers left: [29]). Try possible operations.\n    |- Try 48 + 24 = 72. Add 72 to the number set. Current number set: [72, 29], target: 31, just two numbers left.\n     |- Try 72 + 29 = 101. Evaluate 101 != 31, drop this branch.\n     |- Try 72 - 29 = 43. Evaluate 43 != 31, drop this branch.\n     |- Try 72 * 29 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 29 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 - 24 = 24. Add 24 to the number set. Current number set: [24, 29], target: 31, just two numbers left.\n     |- Try 29 + 24 = 53. Evaluate 53 != 31, drop this branch.\n     |- Try 29 - 24 = 5. Evaluate 5 != 31, drop this branch.\n     |- Try 29 * 24 = 696. Evaluate 696 != 31, drop this branch.\n     |- Try 29 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 24 = 1152. Add 1152 to the number set. Current number set: [1152, 29], target: 31, just two numbers left.\n     |- Try 1152 + 29 = 1181. Evaluate 1181 != 31, drop this branch.\n     |- Try 1152 - 29 = 1123. Evaluate 1123 != 31, drop this branch.\n     |- Try 1152 * 29 = 33408. 33408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1152 \/ 29 = 39.7. 39.7 is a decimal, drop this branch.\n    |- Try 48 \/ 24 = 2. Add 2 to the number set. Current number set: [2, 29], target: 31, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 + 2 = 31\nThe step before: 48 \/ 24 = 2\nThe first step: 42 + 6 = 48\n\nOutput the solution in the required format:\n<Solution>\n42 + 6 = 48\n48 \/ 24 = 2\n29 + 2 = 31\n<\/Solution>\n","item":{"nums":[42,6,29,24],"solution":["42 + 6 = 48","48 \/ 24 = 2","29 + 2 = 31"],"target":31}}
+{"instance_id":"countdown_2k_30","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 16, 32, 36]\nTarget: 47","reference_output":"# Search Procedure\nInitial number set: [37, 16, 32, 36], target: 47. Options for choosing two numbers: [(37, 16), (37, 32), (37, 36), (16, 32), (16, 36), (32, 36)].\n |- Pick two numbers (37, 16) (numbers left: [32, 36]). Try possible operations.\n  |- Try 37 + 16 = 53. Add 53 to the number set. Current number set: [53, 32, 36], target: 47. Options for choosing two numbers: [(53, 32), (53, 36), (32, 36)].\n   |- Pick two numbers (53, 32) (numbers left: [36]). Try possible operations.\n    |- Try 53 + 32 = 85. Add 85 to the number set. Current number set: [85, 36], target: 47, just two numbers left.\n     |- Try 85 + 36 = 121. Evaluate 121 != 47, drop this branch.\n     |- Try 85 - 36 = 49. Evaluate 49 != 47, drop this branch.\n     |- Try 85 * 36 = 3060. 3060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 36 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 53 - 32 = 21. Add 21 to the number set. Current number set: [21, 36], target: 47, just two numbers left.\n     |- Try 36 + 21 = 57. Evaluate 57 != 47, drop this branch.\n     |- Try 36 - 21 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 36 * 21 = 756. Evaluate 756 != 47, drop this branch.\n     |- Try 36 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 53 * 32 = 1696. Add 1696 to the number set. Current number set: [1696, 36], target: 47, just two numbers left.\n     |- Try 1696 + 36 = 1732. Evaluate 1732 != 47, drop this branch.\n     |- Try 1696 - 36 = 1660. Evaluate 1660 != 47, drop this branch.\n     |- Try 1696 * 36 = 61056. 61056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1696 \/ 36 = 47.1. 47.1 is a decimal, drop this branch.\n    |- Try 53 \/ 32 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (53, 36) (numbers left: [32]). Try possible operations.\n    |- Try 53 + 36 = 89. Add 89 to the number set. Current number set: [89, 32], target: 47, just two numbers left.\n     |- Try 89 + 32 = 121. Evaluate 121 != 47, drop this branch.\n     |- Try 89 - 32 = 57. Evaluate 57 != 47, drop this branch.\n     |- Try 89 * 32 = 2848. 2848 exceeds the maximum intermediate result, drop this branch.\n     |- Try 89 \/ 32 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 53 - 36 = 17. Add 17 to the number set. Current number set: [17, 32], target: 47, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 47, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 47, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 53 * 36 = 1908. Add 1908 to the number set. Current number set: [1908, 32], target: 47, just two numbers left.\n     |- Try 1908 + 32 = 1940. Evaluate 1940 != 47, drop this branch.\n     |- Try 1908 - 32 = 1876. Evaluate 1876 != 47, drop this branch.\n     |- Try 1908 * 32 = 61056. 61056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1908 \/ 32 = 59.6. 59.6 is a decimal, drop this branch.\n    |- Try 53 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 36) (numbers left: [53]). Try possible operations.\n    |- Try 36 + 32 = 68. Add 68 to the number set. Current number set: [68, 53], target: 47, just two numbers left.\n     |- Try 68 + 53 = 121. Evaluate 121 != 47, drop this branch.\n     |- Try 68 - 53 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 68 * 53 = 3604. 3604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 53 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 - 32 = 4. Add 4 to the number set. Current number set: [4, 53], target: 47, just two numbers left.\n     |- Try 53 + 4 = 57. Evaluate 57 != 47, drop this branch.\n     |- Try 53 - 4 = 49. Evaluate 49 != 47, drop this branch.\n     |- Try 53 * 4 = 212. Evaluate 212 != 47, drop this branch.\n     |- Try 53 \/ 4 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 36 * 32 = 1152. Add 1152 to the number set. Current number set: [1152, 53], target: 47, just two numbers left.\n     |- Try 1152 + 53 = 1205. Evaluate 1205 != 47, drop this branch.\n     |- Try 1152 - 53 = 1099. Evaluate 1099 != 47, drop this branch.\n     |- Try 1152 * 53 = 61056. 61056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1152 \/ 53 = 21.7. 21.7 is a decimal, drop this branch.\n    |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 37 - 16 = 21. Add 21 to the number set. Current number set: [21, 32, 36], target: 47. Options for choosing two numbers: [(21, 32), (21, 36), (32, 36)].\n   |- Pick two numbers (21, 32) (numbers left: [36]). Try possible operations.\n    |- Try 32 + 21 = 53. Add 53 to the number set. Current number set: [53, 36], target: 47, just two numbers left.\n     |- Try 53 + 36 = 89. Evaluate 89 != 47, drop this branch.\n     |- Try 53 - 36 = 17. Evaluate 17 != 47, drop this branch.\n     |- Try 53 * 36 = 1908. Evaluate 1908 != 47, drop this branch.\n     |- Try 53 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 32 - 21 = 11. Add 11 to the number set. Current number set: [11, 36], target: 47, just two numbers left.\n     |- Try 36 + 11 = 47. Evaluate 47 == 47, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 + 11 = 47\nThe step before: 32 - 21 = 11\nThe first step: 37 - 16 = 21\n\nOutput the solution in the required format:\n<Solution>\n37 - 16 = 21\n32 - 21 = 11\n36 + 11 = 47\n<\/Solution>\n","item":{"nums":[37,16,32,36],"solution":["37 - 16 = 21","32 - 21 = 11","36 + 11 = 47"],"target":47}}
+{"instance_id":"countdown_2k_31","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 30, 24, 4]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [33, 30, 24, 4], target: 31. Options for choosing two numbers: [(33, 30), (33, 24), (33, 4), (30, 24), (30, 4), (24, 4)].\n |- Pick two numbers (33, 30) (numbers left: [24, 4]). Try possible operations.\n  |- Try 33 + 30 = 63. Add 63 to the number set. Current number set: [63, 24, 4], target: 31. Options for choosing two numbers: [(63, 24), (63, 4), (24, 4)].\n   |- Pick two numbers (63, 24) (numbers left: [4]). Try possible operations.\n    |- Try 63 + 24 = 87. Add 87 to the number set. Current number set: [87, 4], target: 31, just two numbers left.\n     |- Try 87 + 4 = 91. Evaluate 91 != 31, drop this branch.\n     |- Try 87 - 4 = 83. Evaluate 83 != 31, drop this branch.\n     |- Try 87 * 4 = 348. Evaluate 348 != 31, drop this branch.\n     |- Try 87 \/ 4 = 21.8. 21.8 is a decimal, drop this branch.\n    |- Try 63 - 24 = 39. Add 39 to the number set. Current number set: [39, 4], target: 31, just two numbers left.\n     |- Try 39 + 4 = 43. Evaluate 43 != 31, drop this branch.\n     |- Try 39 - 4 = 35. Evaluate 35 != 31, drop this branch.\n     |- Try 39 * 4 = 156. Evaluate 156 != 31, drop this branch.\n     |- Try 39 \/ 4 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 63 * 24 = 1512. Add 1512 to the number set. Current number set: [1512, 4], target: 31, just two numbers left.\n     |- Try 1512 + 4 = 1516. Evaluate 1516 != 31, drop this branch.\n     |- Try 1512 - 4 = 1508. Evaluate 1508 != 31, drop this branch.\n     |- Try 1512 * 4 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1512 \/ 4 = 378. Evaluate 378 != 31, drop this branch.\n    |- Try 63 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (63, 4) (numbers left: [24]). Try possible operations.\n    |- Try 63 + 4 = 67. Add 67 to the number set. Current number set: [67, 24], target: 31, just two numbers left.\n     |- Try 67 + 24 = 91. Evaluate 91 != 31, drop this branch.\n     |- Try 67 - 24 = 43. Evaluate 43 != 31, drop this branch.\n     |- Try 67 * 24 = 1608. Evaluate 1608 != 31, drop this branch.\n     |- Try 67 \/ 24 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 63 - 4 = 59. Add 59 to the number set. Current number set: [59, 24], target: 31, just two numbers left.\n     |- Try 59 + 24 = 83. Evaluate 83 != 31, drop this branch.\n     |- Try 59 - 24 = 35. Evaluate 35 != 31, drop this branch.\n     |- Try 59 * 24 = 1416. Evaluate 1416 != 31, drop this branch.\n     |- Try 59 \/ 24 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 63 * 4 = 252. Add 252 to the number set. Current number set: [252, 24], target: 31, just two numbers left.\n     |- Try 252 + 24 = 276. Evaluate 276 != 31, drop this branch.\n     |- Try 252 - 24 = 228. Evaluate 228 != 31, drop this branch.\n     |- Try 252 * 24 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 24 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 63 \/ 4 = 15.8. 15.8 is a decimal, drop this branch.\n   |- Pick two numbers (24, 4) (numbers left: [63]). Try possible operations.\n    |- Try 24 + 4 = 28. Add 28 to the number set. Current number set: [28, 63], target: 31, just two numbers left.\n     |- Try 63 + 28 = 91. Evaluate 91 != 31, drop this branch.\n     |- Try 63 - 28 = 35. Evaluate 35 != 31, drop this branch.\n     |- Try 63 * 28 = 1764. Evaluate 1764 != 31, drop this branch.\n     |- Try 63 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 24 - 4 = 20. Add 20 to the number set. Current number set: [20, 63], target: 31, just two numbers left.\n     |- Try 63 + 20 = 83. Evaluate 83 != 31, drop this branch.\n     |- Try 63 - 20 = 43. Evaluate 43 != 31, drop this branch.\n     |- Try 63 * 20 = 1260. Evaluate 1260 != 31, drop this branch.\n     |- Try 63 \/ 20 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 24 * 4 = 96. Add 96 to the number set. Current number set: [96, 63], target: 31, just two numbers left.\n     |- Try 96 + 63 = 159. Evaluate 159 != 31, drop this branch.\n     |- Try 96 - 63 = 33. Evaluate 33 != 31, drop this branch.\n     |- Try 96 * 63 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 63 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 \/ 4 = 6. Add 6 to the number set. Current number set: [6, 63], target: 31, just two numbers left.\n     |- Try 63 + 6 = 69. Evaluate 69 != 31, drop this branch.\n     |- Try 63 - 6 = 57. Evaluate 57 != 31, drop this branch.\n     |- Try 63 * 6 = 378. Evaluate 378 != 31, drop this branch.\n     |- Try 63 \/ 6 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 33 - 30 = 3. Add 3 to the number set. Current number set: [3, 24, 4], target: 31. Options for choosing two numbers: [(3, 24), (3, 4), (24, 4)].\n   |- Pick two numbers (3, 24) (numbers left: [4]). Try possible operations.\n    |- Try 24 + 3 = 27. Add 27 to the number set. Current number set: [27, 4], target: 31, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 4 = 31\nThe step before: 24 + 3 = 27\nThe first step: 33 - 30 = 3\n\nOutput the solution in the required format:\n<Solution>\n33 - 30 = 3\n24 + 3 = 27\n27 + 4 = 31\n<\/Solution>\n","item":{"nums":[33,30,24,4],"solution":["33 - 30 = 3","24 + 3 = 27","27 + 4 = 31"],"target":31}}
+{"instance_id":"countdown_2k_32","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 43, 40, 31]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [41, 43, 40, 31], target: 49. Options for choosing two numbers: [(41, 43), (41, 40), (41, 31), (43, 40), (43, 31), (40, 31)].\n |- Pick two numbers (41, 43) (numbers left: [40, 31]). Try possible operations.\n  |- Try 43 + 41 = 84. Add 84 to the number set. Current number set: [84, 40, 31], target: 49. Options for choosing two numbers: [(84, 40), (84, 31), (40, 31)].\n   |- Pick two numbers (84, 40) (numbers left: [31]). Try possible operations.\n    |- Try 84 + 40 = 124. Add 124 to the number set. Current number set: [124, 31], target: 49, just two numbers left.\n     |- Try 124 + 31 = 155. Evaluate 155 != 49, drop this branch.\n     |- Try 124 - 31 = 93. Evaluate 93 != 49, drop this branch.\n     |- Try 124 * 31 = 3844. 3844 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 31 = 4. Evaluate 4 != 49, drop this branch.\n    |- Try 84 - 40 = 44. Add 44 to the number set. Current number set: [44, 31], target: 49, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 49, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 44 * 31 = 1364. Evaluate 1364 != 49, drop this branch.\n     |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 84 * 40 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n    |- Try 84 \/ 40 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (84, 31) (numbers left: [40]). Try possible operations.\n    |- Try 84 + 31 = 115. Add 115 to the number set. Current number set: [115, 40], target: 49, just two numbers left.\n     |- Try 115 + 40 = 155. Evaluate 155 != 49, drop this branch.\n     |- Try 115 - 40 = 75. Evaluate 75 != 49, drop this branch.\n     |- Try 115 * 40 = 4600. 4600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 40 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 84 - 31 = 53. Add 53 to the number set. Current number set: [53, 40], target: 49, just two numbers left.\n     |- Try 53 + 40 = 93. Evaluate 93 != 49, drop this branch.\n     |- Try 53 - 40 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 53 * 40 = 2120. 2120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 40 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 84 * 31 = 2604. 2604 exceeds the maximum intermediate result, drop this branch.\n    |- Try 84 \/ 31 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (40, 31) (numbers left: [84]). Try possible operations.\n    |- Try 40 + 31 = 71. Add 71 to the number set. Current number set: [71, 84], target: 49, just two numbers left.\n     |- Try 84 + 71 = 155. Evaluate 155 != 49, drop this branch.\n     |- Try 84 - 71 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 84 * 71 = 5964. 5964 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 71 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 31 = 9. Add 9 to the number set. Current number set: [9, 84], target: 49, just two numbers left.\n     |- Try 84 + 9 = 93. Evaluate 93 != 49, drop this branch.\n     |- Try 84 - 9 = 75. Evaluate 75 != 49, drop this branch.\n     |- Try 84 * 9 = 756. Evaluate 756 != 49, drop this branch.\n     |- Try 84 \/ 9 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 40 * 31 = 1240. Add 1240 to the number set. Current number set: [1240, 84], target: 49, just two numbers left.\n     |- Try 1240 + 84 = 1324. Evaluate 1324 != 49, drop this branch.\n     |- Try 1240 - 84 = 1156. Evaluate 1156 != 49, drop this branch.\n     |- Try 1240 * 84 = 104160. 104160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1240 \/ 84 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 40 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 43 - 41 = 2. Add 2 to the number set. Current number set: [2, 40, 31], target: 49. Options for choosing two numbers: [(2, 40), (2, 31), (40, 31)].\n   |- Pick two numbers (2, 40) (numbers left: [31]). Try possible operations.\n    |- Try 40 + 2 = 42. Add 42 to the number set. Current number set: [42, 31], target: 49, just two numbers left.\n     |- Try 42 + 31 = 73. Evaluate 73 != 49, drop this branch.\n     |- Try 42 - 31 = 11. Evaluate 11 != 49, drop this branch.\n     |- Try 42 * 31 = 1302. Evaluate 1302 != 49, drop this branch.\n     |- Try 42 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 - 2 = 38. Add 38 to the number set. Current number set: [38, 31], target: 49, just two numbers left.\n     |- Try 38 + 31 = 69. Evaluate 69 != 49, drop this branch.\n     |- Try 38 - 31 = 7. Evaluate 7 != 49, drop this branch.\n     |- Try 38 * 31 = 1178. Evaluate 1178 != 49, drop this branch.\n     |- Try 38 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 * 2 = 80. Add 80 to the number set. Current number set: [80, 31], target: 49, just two numbers left.\n     |- Try 80 + 31 = 111. Evaluate 111 != 49, drop this branch.\n     |- Try 80 - 31 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 80 - 31 = 49\nThe step before: 40 * 2 = 80\nThe first step: 43 - 41 = 2\n\nOutput the solution in the required format:\n<Solution>\n43 - 41 = 2\n40 * 2 = 80\n80 - 31 = 49\n<\/Solution>\n","item":{"nums":[41,43,40,31],"solution":["43 - 41 = 2","40 * 2 = 80","80 - 31 = 49"],"target":49}}
+{"instance_id":"countdown_2k_33","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 24, 26, 30]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [6, 24, 26, 30], target: 27. Options for choosing two numbers: [(6, 24), (6, 26), (6, 30), (24, 26), (24, 30), (26, 30)].\n |- Pick two numbers (6, 24) (numbers left: [26, 30]). Try possible operations.\n  |- Try 24 + 6 = 30. Add 30 to the number set. Current number set: [30, 26, 30], target: 27. Options for choosing two numbers: [(30, 26), (30, 30), (26, 30)].\n   |- Pick two numbers (30, 26) (numbers left: [30]). Try possible operations.\n    |- Try 30 + 26 = 56. Add 56 to the number set. Current number set: [56, 30], target: 27, just two numbers left.\n     |- Try 56 + 30 = 86. Evaluate 86 != 27, drop this branch.\n     |- Try 56 - 30 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 56 * 30 = 1680. Evaluate 1680 != 27, drop this branch.\n     |- Try 56 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 - 26 = 4. Add 4 to the number set. Current number set: [4, 30], target: 27, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 27, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 30 * 26 = 780. Add 780 to the number set. Current number set: [780, 30], target: 27, just two numbers left.\n     |- Try 780 + 30 = 810. Evaluate 810 != 27, drop this branch.\n     |- Try 780 - 30 = 750. Evaluate 750 != 27, drop this branch.\n     |- Try 780 * 30 = 23400. 23400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 780 \/ 30 = 26. Evaluate 26 != 27, drop this branch.\n    |- Try 30 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (30, 30) (numbers left: [26]). Try possible operations.\n    |- Try 30 + 30 = 60. Add 60 to the number set. Current number set: [60, 26], target: 27, just two numbers left.\n     |- Try 60 + 26 = 86. Evaluate 86 != 27, drop this branch.\n     |- Try 60 - 26 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 60 * 26 = 1560. Evaluate 1560 != 27, drop this branch.\n     |- Try 60 \/ 26 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 30 - 30 = 0. Add 0 to the number set. Current number set: [0, 26], target: 27, just two numbers left.\n     |- Try 26 + 0 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 26 - 0 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 26 * 0 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 26 \/ 0 (invalid operation). drop this branch.\n    |- Try 30 * 30 = 900. Add 900 to the number set. Current number set: [900, 26], target: 27, just two numbers left.\n     |- Try 900 + 26 = 926. Evaluate 926 != 27, drop this branch.\n     |- Try 900 - 26 = 874. Evaluate 874 != 27, drop this branch.\n     |- Try 900 * 26 = 23400. 23400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 900 \/ 26 = 34.6. 34.6 is a decimal, drop this branch.\n    |- Try 30 \/ 30 = 1. Add 1 to the number set. Current number set: [1, 26], target: 27, just two numbers left.\n     |- Try 26 + 1 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 + 1 = 27\nThe step before: 30 \/ 30 = 1\nThe first step: 24 + 6 = 30\n\nOutput the solution in the required format:\n<Solution>\n24 + 6 = 30\n30 \/ 30 = 1\n26 + 1 = 27\n<\/Solution>\n","item":{"nums":[6,24,26,30],"solution":["24 + 6 = 30","30 \/ 30 = 1","26 + 1 = 27"],"target":27}}
+{"instance_id":"countdown_2k_34","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 6, 42, 42]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [44, 6, 42, 42], target: 46. Options for choosing two numbers: [(44, 6), (44, 42), (44, 42), (6, 42), (6, 42), (42, 42)].\n |- Pick two numbers (44, 6) (numbers left: [42, 42]). Try possible operations.\n  |- Try 44 + 6 = 50. Add 50 to the number set. Current number set: [50, 42, 42], target: 46. Options for choosing two numbers: [(50, 42), (50, 42), (42, 42)].\n   |- Pick two numbers (50, 42) (numbers left: [42]). Try possible operations.\n    |- Try 50 + 42 = 92. Add 92 to the number set. Current number set: [92, 42], target: 46, just two numbers left.\n     |- Try 92 + 42 = 134. Evaluate 134 != 46, drop this branch.\n     |- Try 92 - 42 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 92 * 42 = 3864. 3864 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 42 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 50 - 42 = 8. Add 8 to the number set. Current number set: [8, 42], target: 46, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 46, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 50 * 42 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (50, 42) (numbers left: [42]). Try possible operations.\n    |- Try 50 + 42 = 92. Add 92 to the number set. Current number set: [92, 42], target: 46, just two numbers left.\n     |- Try 92 + 42 = 134. Evaluate 134 != 46, drop this branch.\n     |- Try 92 - 42 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 92 * 42 = 3864. 3864 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 42 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 50 - 42 = 8. Add 8 to the number set. Current number set: [8, 42], target: 46, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 46, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 50 * 42 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 42) (numbers left: [50]). Try possible operations.\n    |- Try 42 + 42 = 84. Add 84 to the number set. Current number set: [84, 50], target: 46, just two numbers left.\n     |- Try 84 + 50 = 134. Evaluate 134 != 46, drop this branch.\n     |- Try 84 - 50 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 84 * 50 = 4200. 4200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 50 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 42 - 42 = 0. Add 0 to the number set. Current number set: [0, 50], target: 46, just two numbers left.\n     |- Try 50 + 0 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 50 - 0 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 50 * 0 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 50 \/ 0 (invalid operation). drop this branch.\n    |- Try 42 * 42 = 1764. Add 1764 to the number set. Current number set: [1764, 50], target: 46, just two numbers left.\n     |- Try 1764 + 50 = 1814. Evaluate 1814 != 46, drop this branch.\n     |- Try 1764 - 50 = 1714. Evaluate 1714 != 46, drop this branch.\n     |- Try 1764 * 50 = 88200. 88200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1764 \/ 50 = 35.3. 35.3 is a decimal, drop this branch.\n    |- Try 42 \/ 42 = 1. Add 1 to the number set. Current number set: [1, 50], target: 46, just two numbers left.\n     |- Try 50 + 1 = 51. Evaluate 51 != 46, drop this branch.\n     |- Try 50 - 1 = 49. Evaluate 49 != 46, drop this branch.\n     |- Try 50 * 1 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 50 \/ 1 = 50. Evaluate 50 != 46, drop this branch.\n  |- Try 44 - 6 = 38. Add 38 to the number set. Current number set: [38, 42, 42], target: 46. Options for choosing two numbers: [(38, 42), (38, 42), (42, 42)].\n   |- Pick two numbers (38, 42) (numbers left: [42]). Try possible operations.\n    |- Try 42 + 38 = 80. Add 80 to the number set. Current number set: [80, 42], target: 46, just two numbers left.\n     |- Try 80 + 42 = 122. Evaluate 122 != 46, drop this branch.\n     |- Try 80 - 42 = 38. Evaluate 38 != 46, drop this branch.\n     |- Try 80 * 42 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 42 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 42 - 38 = 4. Add 4 to the number set. Current number set: [4, 42], target: 46, just two numbers left.\n     |- Try 42 + 4 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 42 + 4 = 46\nThe step before: 42 - 38 = 4\nThe first step: 44 - 6 = 38\n\nOutput the solution in the required format:\n<Solution>\n44 - 6 = 38\n42 - 38 = 4\n42 + 4 = 46\n<\/Solution>\n","item":{"nums":[44,6,42,42],"solution":["44 - 6 = 38","42 - 38 = 4","42 + 4 = 46"],"target":46}}
+{"instance_id":"countdown_2k_35","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 7, 34, 3]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [37, 7, 34, 3], target: 12. Options for choosing two numbers: [(37, 7), (37, 34), (37, 3), (7, 34), (7, 3), (34, 3)].\n |- Pick two numbers (37, 7) (numbers left: [34, 3]). Try possible operations.\n  |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 34, 3], target: 12. Options for choosing two numbers: [(44, 34), (44, 3), (34, 3)].\n   |- Pick two numbers (44, 34) (numbers left: [3]). Try possible operations.\n    |- Try 44 + 34 = 78. Add 78 to the number set. Current number set: [78, 3], target: 12, just two numbers left.\n     |- Try 78 + 3 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 78 - 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 78 * 3 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 78 \/ 3 = 26. Evaluate 26 != 12, drop this branch.\n    |- Try 44 - 34 = 10. Add 10 to the number set. Current number set: [10, 3], target: 12, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 12, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 44 * 34 = 1496. Add 1496 to the number set. Current number set: [1496, 3], target: 12, just two numbers left.\n     |- Try 1496 + 3 = 1499. Evaluate 1499 != 12, drop this branch.\n     |- Try 1496 - 3 = 1493. Evaluate 1493 != 12, drop this branch.\n     |- Try 1496 * 3 = 4488. 4488 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1496 \/ 3 = 498.7. 498.7 is a decimal, drop this branch.\n    |- Try 44 \/ 34 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (44, 3) (numbers left: [34]). Try possible operations.\n    |- Try 44 + 3 = 47. Add 47 to the number set. Current number set: [47, 34], target: 12, just two numbers left.\n     |- Try 47 + 34 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 47 - 34 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 47 * 34 = 1598. Evaluate 1598 != 12, drop this branch.\n     |- Try 47 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 3 = 41. Add 41 to the number set. Current number set: [41, 34], target: 12, just two numbers left.\n     |- Try 41 + 34 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 41 - 34 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 41 * 34 = 1394. Evaluate 1394 != 12, drop this branch.\n     |- Try 41 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 3 = 132. Add 132 to the number set. Current number set: [132, 34], target: 12, just two numbers left.\n     |- Try 132 + 34 = 166. Evaluate 166 != 12, drop this branch.\n     |- Try 132 - 34 = 98. Evaluate 98 != 12, drop this branch.\n     |- Try 132 * 34 = 4488. 4488 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 34 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 44 \/ 3 = 14.7. 14.7 is a decimal, drop this branch.\n   |- Pick two numbers (34, 3) (numbers left: [44]). Try possible operations.\n    |- Try 34 + 3 = 37. Add 37 to the number set. Current number set: [37, 44], target: 12, just two numbers left.\n     |- Try 44 + 37 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 44 - 37 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 44 * 37 = 1628. Evaluate 1628 != 12, drop this branch.\n     |- Try 44 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 34 - 3 = 31. Add 31 to the number set. Current number set: [31, 44], target: 12, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 44 * 31 = 1364. Evaluate 1364 != 12, drop this branch.\n     |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 34 * 3 = 102. Add 102 to the number set. Current number set: [102, 44], target: 12, just two numbers left.\n     |- Try 102 + 44 = 146. Evaluate 146 != 12, drop this branch.\n     |- Try 102 - 44 = 58. Evaluate 58 != 12, drop this branch.\n     |- Try 102 * 44 = 4488. 4488 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 44 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n  |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 34, 3], target: 12. Options for choosing two numbers: [(30, 34), (30, 3), (34, 3)].\n   |- Pick two numbers (30, 34) (numbers left: [3]). Try possible operations.\n    |- Try 34 + 30 = 64. Add 64 to the number set. Current number set: [64, 3], target: 12, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 12, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 12, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 34 - 30 = 4. Add 4 to the number set. Current number set: [4, 3], target: 12, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 4 * 3 = 12\nThe step before: 34 - 30 = 4\nThe first step: 37 - 7 = 30\n\nOutput the solution in the required format:\n<Solution>\n37 - 7 = 30\n34 - 30 = 4\n4 * 3 = 12\n<\/Solution>\n","item":{"nums":[37,7,34,3],"solution":["37 - 7 = 30","34 - 30 = 4","4 * 3 = 12"],"target":12}}
+{"instance_id":"countdown_2k_36","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 3, 5, 44]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [18, 3, 5, 44], target: 24. Options for choosing two numbers: [(18, 3), (18, 5), (18, 44), (3, 5), (3, 44), (5, 44)].\n |- Pick two numbers (18, 3) (numbers left: [5, 44]). Try possible operations.\n  |- Try 18 + 3 = 21. Add 21 to the number set. Current number set: [21, 5, 44], target: 24. Options for choosing two numbers: [(21, 5), (21, 44), (5, 44)].\n   |- Pick two numbers (21, 5) (numbers left: [44]). Try possible operations.\n    |- Try 21 + 5 = 26. Add 26 to the number set. Current number set: [26, 44], target: 24, just two numbers left.\n     |- Try 44 + 26 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 44 - 26 = 18. Evaluate 18 != 24, drop this branch.\n     |- Try 44 * 26 = 1144. Evaluate 1144 != 24, drop this branch.\n     |- Try 44 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 - 5 = 16. Add 16 to the number set. Current number set: [16, 44], target: 24, just two numbers left.\n     |- Try 44 + 16 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 44 - 16 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 44 * 16 = 704. Evaluate 704 != 24, drop this branch.\n     |- Try 44 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 21 * 5 = 105. Add 105 to the number set. Current number set: [105, 44], target: 24, just two numbers left.\n     |- Try 105 + 44 = 149. Evaluate 149 != 24, drop this branch.\n     |- Try 105 - 44 = 61. Evaluate 61 != 24, drop this branch.\n     |- Try 105 * 44 = 4620. 4620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 44 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 21 \/ 5 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (21, 44) (numbers left: [5]). Try possible operations.\n    |- Try 44 + 21 = 65. Add 65 to the number set. Current number set: [65, 5], target: 24, just two numbers left.\n     |- Try 65 + 5 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 65 - 5 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 65 * 5 = 325. Evaluate 325 != 24, drop this branch.\n     |- Try 65 \/ 5 = 13. Evaluate 13 != 24, drop this branch.\n    |- Try 44 - 21 = 23. Add 23 to the number set. Current number set: [23, 5], target: 24, just two numbers left.\n     |- Try 23 + 5 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 23 - 5 = 18. Evaluate 18 != 24, drop this branch.\n     |- Try 23 * 5 = 115. Evaluate 115 != 24, drop this branch.\n     |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 44 * 21 = 924. Add 924 to the number set. Current number set: [924, 5], target: 24, just two numbers left.\n     |- Try 924 + 5 = 929. Evaluate 929 != 24, drop this branch.\n     |- Try 924 - 5 = 919. Evaluate 919 != 24, drop this branch.\n     |- Try 924 * 5 = 4620. 4620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 5 = 184.8. 184.8 is a decimal, drop this branch.\n    |- Try 44 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (5, 44) (numbers left: [21]). Try possible operations.\n    |- Try 44 + 5 = 49. Add 49 to the number set. Current number set: [49, 21], target: 24, just two numbers left.\n     |- Try 49 + 21 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 49 - 21 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 49 * 21 = 1029. Evaluate 1029 != 24, drop this branch.\n     |- Try 49 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 44 - 5 = 39. Add 39 to the number set. Current number set: [39, 21], target: 24, just two numbers left.\n     |- Try 39 + 21 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 39 - 21 = 18. Evaluate 18 != 24, drop this branch.\n     |- Try 39 * 21 = 819. Evaluate 819 != 24, drop this branch.\n     |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 * 5 = 220. Add 220 to the number set. Current number set: [220, 21], target: 24, just two numbers left.\n     |- Try 220 + 21 = 241. Evaluate 241 != 24, drop this branch.\n     |- Try 220 - 21 = 199. Evaluate 199 != 24, drop this branch.\n     |- Try 220 * 21 = 4620. 4620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 21 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 44 \/ 5 = 8.8. 8.8 is a decimal, drop this branch.\n  |- Try 18 - 3 = 15. Add 15 to the number set. Current number set: [15, 5, 44], target: 24. Options for choosing two numbers: [(15, 5), (15, 44), (5, 44)].\n   |- Pick two numbers (15, 5) (numbers left: [44]). Try possible operations.\n    |- Try 15 + 5 = 20. Add 20 to the number set. Current number set: [20, 44], target: 24, just two numbers left.\n     |- Try 44 + 20 = 64. Evaluate 64 != 24, drop this branch.\n     |- Try 44 - 20 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 20 = 24\nThe step before: 15 + 5 = 20\nThe first step: 18 - 3 = 15\n\nOutput the solution in the required format:\n<Solution>\n18 - 3 = 15\n15 + 5 = 20\n44 - 20 = 24\n<\/Solution>\n","item":{"nums":[18,3,5,44],"solution":["18 - 3 = 15","15 + 5 = 20","44 - 20 = 24"],"target":24}}
+{"instance_id":"countdown_2k_37","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 7, 2, 6]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [27, 7, 2, 6], target: 37. Options for choosing two numbers: [(27, 7), (27, 2), (27, 6), (7, 2), (7, 6), (2, 6)].\n |- Pick two numbers (27, 7) (numbers left: [2, 6]). Try possible operations.\n  |- Try 27 + 7 = 34. Add 34 to the number set. Current number set: [34, 2, 6], target: 37. Options for choosing two numbers: [(34, 2), (34, 6), (2, 6)].\n   |- Pick two numbers (34, 2) (numbers left: [6]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 6], target: 37, just two numbers left.\n     |- Try 36 + 6 = 42. Evaluate 42 != 37, drop this branch.\n     |- Try 36 - 6 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 36 * 6 = 216. Evaluate 216 != 37, drop this branch.\n     |- Try 36 \/ 6 = 6. Evaluate 6 != 37, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 6], target: 37, just two numbers left.\n     |- Try 32 + 6 = 38. Evaluate 38 != 37, drop this branch.\n     |- Try 32 - 6 = 26. Evaluate 26 != 37, drop this branch.\n     |- Try 32 * 6 = 192. Evaluate 192 != 37, drop this branch.\n     |- Try 32 \/ 6 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 6], target: 37, just two numbers left.\n     |- Try 68 + 6 = 74. Evaluate 74 != 37, drop this branch.\n     |- Try 68 - 6 = 62. Evaluate 62 != 37, drop this branch.\n     |- Try 68 * 6 = 408. Evaluate 408 != 37, drop this branch.\n     |- Try 68 \/ 6 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 34 \/ 2 = 17. Add 17 to the number set. Current number set: [17, 6], target: 37, just two numbers left.\n     |- Try 17 + 6 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 17 - 6 = 11. Evaluate 11 != 37, drop this branch.\n     |- Try 17 * 6 = 102. Evaluate 102 != 37, drop this branch.\n     |- Try 17 \/ 6 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (34, 6) (numbers left: [2]). Try possible operations.\n    |- Try 34 + 6 = 40. Add 40 to the number set. Current number set: [40, 2], target: 37, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 37, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 37, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 37, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 37, drop this branch.\n    |- Try 34 - 6 = 28. Add 28 to the number set. Current number set: [28, 2], target: 37, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 37, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 37, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 != 37, drop this branch.\n    |- Try 34 * 6 = 204. Add 204 to the number set. Current number set: [204, 2], target: 37, just two numbers left.\n     |- Try 204 + 2 = 206. Evaluate 206 != 37, drop this branch.\n     |- Try 204 - 2 = 202. Evaluate 202 != 37, drop this branch.\n     |- Try 204 * 2 = 408. Evaluate 408 != 37, drop this branch.\n     |- Try 204 \/ 2 = 102. Evaluate 102 != 37, drop this branch.\n    |- Try 34 \/ 6 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (2, 6) (numbers left: [34]). Try possible operations.\n    |- Try 6 + 2 = 8. Add 8 to the number set. Current number set: [8, 34], target: 37, just two numbers left.\n     |- Try 34 + 8 = 42. Evaluate 42 != 37, drop this branch.\n     |- Try 34 - 8 = 26. Evaluate 26 != 37, drop this branch.\n     |- Try 34 * 8 = 272. Evaluate 272 != 37, drop this branch.\n     |- Try 34 \/ 8 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 6 - 2 = 4. Add 4 to the number set. Current number set: [4, 34], target: 37, just two numbers left.\n     |- Try 34 + 4 = 38. Evaluate 38 != 37, drop this branch.\n     |- Try 34 - 4 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 34 * 4 = 136. Evaluate 136 != 37, drop this branch.\n     |- Try 34 \/ 4 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 6 * 2 = 12. Add 12 to the number set. Current number set: [12, 34], target: 37, just two numbers left.\n     |- Try 34 + 12 = 46. Evaluate 46 != 37, drop this branch.\n     |- Try 34 - 12 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 34 * 12 = 408. Evaluate 408 != 37, drop this branch.\n     |- Try 34 \/ 12 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 6 \/ 2 = 3. Add 3 to the number set. Current number set: [3, 34], target: 37, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 3 = 37\nThe step before: 6 \/ 2 = 3\nThe first step: 27 + 7 = 34\n\nOutput the solution in the required format:\n<Solution>\n27 + 7 = 34\n6 \/ 2 = 3\n34 + 3 = 37\n<\/Solution>\n","item":{"nums":[27,7,2,6],"solution":["27 + 7 = 34","6 \/ 2 = 3","34 + 3 = 37"],"target":37}}
+{"instance_id":"countdown_2k_38","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 3, 18, 15]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [19, 3, 18, 15], target: 49. Options for choosing two numbers: [(19, 3), (19, 18), (19, 15), (3, 18), (3, 15), (18, 15)].\n |- Pick two numbers (19, 3) (numbers left: [18, 15]). Try possible operations.\n  |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 18, 15], target: 49. Options for choosing two numbers: [(22, 18), (22, 15), (18, 15)].\n   |- Pick two numbers (22, 18) (numbers left: [15]). Try possible operations.\n    |- Try 22 + 18 = 40. Add 40 to the number set. Current number set: [40, 15], target: 49, just two numbers left.\n     |- Try 40 + 15 = 55. Evaluate 55 != 49, drop this branch.\n     |- Try 40 - 15 = 25. Evaluate 25 != 49, drop this branch.\n     |- Try 40 * 15 = 600. Evaluate 600 != 49, drop this branch.\n     |- Try 40 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 22 - 18 = 4. Add 4 to the number set. Current number set: [4, 15], target: 49, just two numbers left.\n     |- Try 15 + 4 = 19. Evaluate 19 != 49, drop this branch.\n     |- Try 15 - 4 = 11. Evaluate 11 != 49, drop this branch.\n     |- Try 15 * 4 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 15 \/ 4 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 22 * 18 = 396. Add 396 to the number set. Current number set: [396, 15], target: 49, just two numbers left.\n     |- Try 396 + 15 = 411. Evaluate 411 != 49, drop this branch.\n     |- Try 396 - 15 = 381. Evaluate 381 != 49, drop this branch.\n     |- Try 396 * 15 = 5940. 5940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 15 = 26.4. 26.4 is a decimal, drop this branch.\n    |- Try 22 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (22, 15) (numbers left: [18]). Try possible operations.\n    |- Try 22 + 15 = 37. Add 37 to the number set. Current number set: [37, 18], target: 49, just two numbers left.\n     |- Try 37 + 18 = 55. Evaluate 55 != 49, drop this branch.\n     |- Try 37 - 18 = 19. Evaluate 19 != 49, drop this branch.\n     |- Try 37 * 18 = 666. Evaluate 666 != 49, drop this branch.\n     |- Try 37 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 22 - 15 = 7. Add 7 to the number set. Current number set: [7, 18], target: 49, just two numbers left.\n     |- Try 18 + 7 = 25. Evaluate 25 != 49, drop this branch.\n     |- Try 18 - 7 = 11. Evaluate 11 != 49, drop this branch.\n     |- Try 18 * 7 = 126. Evaluate 126 != 49, drop this branch.\n     |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 22 * 15 = 330. Add 330 to the number set. Current number set: [330, 18], target: 49, just two numbers left.\n     |- Try 330 + 18 = 348. Evaluate 348 != 49, drop this branch.\n     |- Try 330 - 18 = 312. Evaluate 312 != 49, drop this branch.\n     |- Try 330 * 18 = 5940. 5940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 18 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 15) (numbers left: [22]). Try possible operations.\n    |- Try 18 + 15 = 33. Add 33 to the number set. Current number set: [33, 22], target: 49, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 49, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 49, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 49, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 - 15 = 3. Add 3 to the number set. Current number set: [3, 22], target: 49, just two numbers left.\n     |- Try 22 + 3 = 25. Evaluate 25 != 49, drop this branch.\n     |- Try 22 - 3 = 19. Evaluate 19 != 49, drop this branch.\n     |- Try 22 * 3 = 66. Evaluate 66 != 49, drop this branch.\n     |- Try 22 \/ 3 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 18 * 15 = 270. Add 270 to the number set. Current number set: [270, 22], target: 49, just two numbers left.\n     |- Try 270 + 22 = 292. Evaluate 292 != 49, drop this branch.\n     |- Try 270 - 22 = 248. Evaluate 248 != 49, drop this branch.\n     |- Try 270 * 22 = 5940. 5940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 22 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 18 \/ 15 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 18, 15], target: 49. Options for choosing two numbers: [(16, 18), (16, 15), (18, 15)].\n   |- Pick two numbers (16, 18) (numbers left: [15]). Try possible operations.\n    |- Try 18 + 16 = 34. Add 34 to the number set. Current number set: [34, 15], target: 49, just two numbers left.\n     |- Try 34 + 15 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 15 = 49\nThe step before: 18 + 16 = 34\nThe first step: 19 - 3 = 16\n\nOutput the solution in the required format:\n<Solution>\n19 - 3 = 16\n18 + 16 = 34\n34 + 15 = 49\n<\/Solution>\n","item":{"nums":[19,3,18,15],"solution":["19 - 3 = 16","18 + 16 = 34","34 + 15 = 49"],"target":49}}
+{"instance_id":"countdown_2k_39","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 1, 45, 22]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [1, 1, 45, 22], target: 23. Options for choosing two numbers: [(1, 1), (1, 45), (1, 22), (1, 45), (1, 22), (45, 22)].\n |- Pick two numbers (1, 1) (numbers left: [45, 22]). Try possible operations.\n  |- Try 1 + 1 = 2. Add 2 to the number set. Current number set: [2, 45, 22], target: 23. Options for choosing two numbers: [(2, 45), (2, 22), (45, 22)].\n   |- Pick two numbers (2, 45) (numbers left: [22]). Try possible operations.\n    |- Try 45 + 2 = 47. Add 47 to the number set. Current number set: [47, 22], target: 23, just two numbers left.\n     |- Try 47 + 22 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 47 - 22 = 25. Evaluate 25 != 23, drop this branch.\n     |- Try 47 * 22 = 1034. Evaluate 1034 != 23, drop this branch.\n     |- Try 47 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 45 - 2 = 43. Add 43 to the number set. Current number set: [43, 22], target: 23, just two numbers left.\n     |- Try 43 + 22 = 65. Evaluate 65 != 23, drop this branch.\n     |- Try 43 - 22 = 21. Evaluate 21 != 23, drop this branch.\n     |- Try 43 * 22 = 946. Evaluate 946 != 23, drop this branch.\n     |- Try 43 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 45 * 2 = 90. Add 90 to the number set. Current number set: [90, 22], target: 23, just two numbers left.\n     |- Try 90 + 22 = 112. Evaluate 112 != 23, drop this branch.\n     |- Try 90 - 22 = 68. Evaluate 68 != 23, drop this branch.\n     |- Try 90 * 22 = 1980. Evaluate 1980 != 23, drop this branch.\n     |- Try 90 \/ 22 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 22) (numbers left: [45]). Try possible operations.\n    |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 45], target: 23, just two numbers left.\n     |- Try 45 + 24 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 45 - 24 = 21. Evaluate 21 != 23, drop this branch.\n     |- Try 45 * 24 = 1080. Evaluate 1080 != 23, drop this branch.\n     |- Try 45 \/ 24 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 45], target: 23, just two numbers left.\n     |- Try 45 + 20 = 65. Evaluate 65 != 23, drop this branch.\n     |- Try 45 - 20 = 25. Evaluate 25 != 23, drop this branch.\n     |- Try 45 * 20 = 900. Evaluate 900 != 23, drop this branch.\n     |- Try 45 \/ 20 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 45], target: 23, just two numbers left.\n     |- Try 45 + 44 = 89. Evaluate 89 != 23, drop this branch.\n     |- Try 45 - 44 = 1. Evaluate 1 != 23, drop this branch.\n     |- Try 45 * 44 = 1980. Evaluate 1980 != 23, drop this branch.\n     |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 45], target: 23, just two numbers left.\n     |- Try 45 + 11 = 56. Evaluate 56 != 23, drop this branch.\n     |- Try 45 - 11 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 45 * 11 = 495. Evaluate 495 != 23, drop this branch.\n     |- Try 45 \/ 11 = 4.1. 4.1 is a decimal, drop this branch.\n   |- Pick two numbers (45, 22) (numbers left: [2]). Try possible operations.\n    |- Try 45 + 22 = 67. Add 67 to the number set. Current number set: [67, 2], target: 23, just two numbers left.\n     |- Try 67 + 2 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 67 - 2 = 65. Evaluate 65 != 23, drop this branch.\n     |- Try 67 * 2 = 134. Evaluate 134 != 23, drop this branch.\n     |- Try 67 \/ 2 = 33.5. 33.5 is a decimal, drop this branch.\n    |- Try 45 - 22 = 23. Add 23 to the number set. Current number set: [23, 2], target: 23, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 != 23, drop this branch.\n     |- Try 23 - 2 = 21. Evaluate 21 != 23, drop this branch.\n     |- Try 23 * 2 = 46. Evaluate 46 != 23, drop this branch.\n     |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 45 * 22 = 990. Add 990 to the number set. Current number set: [990, 2], target: 23, just two numbers left.\n     |- Try 990 + 2 = 992. Evaluate 992 != 23, drop this branch.\n     |- Try 990 - 2 = 988. Evaluate 988 != 23, drop this branch.\n     |- Try 990 * 2 = 1980. Evaluate 1980 != 23, drop this branch.\n     |- Try 990 \/ 2 = 495. Evaluate 495 != 23, drop this branch.\n    |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n  |- Try 1 - 1 = 0. Add 0 to the number set. Current number set: [0, 45, 22], target: 23. Options for choosing two numbers: [(0, 45), (0, 22), (45, 22)].\n   |- Pick two numbers (0, 45) (numbers left: [22]). Try possible operations.\n    |- Try 45 + 0 = 45. Add 45 to the number set. Current number set: [45, 22], target: 23, just two numbers left.\n     |- Try 45 + 22 = 67. Evaluate 67 != 23, drop this branch.\n     |- Try 45 - 22 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 45 - 22 = 23\nThe step before: 45 + 0 = 45\nThe first step: 1 - 1 = 0\n\nOutput the solution in the required format:\n<Solution>\n1 - 1 = 0\n45 + 0 = 45\n45 - 22 = 23\n<\/Solution>\n","item":{"nums":[1,1,45,22],"solution":["1 - 1 = 0","45 + 0 = 45","45 - 22 = 23"],"target":23}}
+{"instance_id":"countdown_2k_40","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 28, 21, 9]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [23, 28, 21, 9], target: 17. Options for choosing two numbers: [(23, 28), (23, 21), (23, 9), (28, 21), (28, 9), (21, 9)].\n |- Pick two numbers (23, 28) (numbers left: [21, 9]). Try possible operations.\n  |- Try 28 + 23 = 51. Add 51 to the number set. Current number set: [51, 21, 9], target: 17. Options for choosing two numbers: [(51, 21), (51, 9), (21, 9)].\n   |- Pick two numbers (51, 21) (numbers left: [9]). Try possible operations.\n    |- Try 51 + 21 = 72. Add 72 to the number set. Current number set: [72, 9], target: 17, just two numbers left.\n     |- Try 72 + 9 = 81. Evaluate 81 != 17, drop this branch.\n     |- Try 72 - 9 = 63. Evaluate 63 != 17, drop this branch.\n     |- Try 72 * 9 = 648. Evaluate 648 != 17, drop this branch.\n     |- Try 72 \/ 9 = 8. Evaluate 8 != 17, drop this branch.\n    |- Try 51 - 21 = 30. Add 30 to the number set. Current number set: [30, 9], target: 17, just two numbers left.\n     |- Try 30 + 9 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 30 - 9 = 21. Evaluate 21 != 17, drop this branch.\n     |- Try 30 * 9 = 270. Evaluate 270 != 17, drop this branch.\n     |- Try 30 \/ 9 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 51 * 21 = 1071. Add 1071 to the number set. Current number set: [1071, 9], target: 17, just two numbers left.\n     |- Try 1071 + 9 = 1080. Evaluate 1080 != 17, drop this branch.\n     |- Try 1071 - 9 = 1062. Evaluate 1062 != 17, drop this branch.\n     |- Try 1071 * 9 = 9639. 9639 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1071 \/ 9 = 119. Evaluate 119 != 17, drop this branch.\n    |- Try 51 \/ 21 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (51, 9) (numbers left: [21]). Try possible operations.\n    |- Try 51 + 9 = 60. Add 60 to the number set. Current number set: [60, 21], target: 17, just two numbers left.\n     |- Try 60 + 21 = 81. Evaluate 81 != 17, drop this branch.\n     |- Try 60 - 21 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 60 * 21 = 1260. Evaluate 1260 != 17, drop this branch.\n     |- Try 60 \/ 21 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 51 - 9 = 42. Add 42 to the number set. Current number set: [42, 21], target: 17, just two numbers left.\n     |- Try 42 + 21 = 63. Evaluate 63 != 17, drop this branch.\n     |- Try 42 - 21 = 21. Evaluate 21 != 17, drop this branch.\n     |- Try 42 * 21 = 882. Evaluate 882 != 17, drop this branch.\n     |- Try 42 \/ 21 = 2. Evaluate 2 != 17, drop this branch.\n    |- Try 51 * 9 = 459. Add 459 to the number set. Current number set: [459, 21], target: 17, just two numbers left.\n     |- Try 459 + 21 = 480. Evaluate 480 != 17, drop this branch.\n     |- Try 459 - 21 = 438. Evaluate 438 != 17, drop this branch.\n     |- Try 459 * 21 = 9639. 9639 exceeds the maximum intermediate result, drop this branch.\n     |- Try 459 \/ 21 = 21.9. 21.9 is a decimal, drop this branch.\n    |- Try 51 \/ 9 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (21, 9) (numbers left: [51]). Try possible operations.\n    |- Try 21 + 9 = 30. Add 30 to the number set. Current number set: [30, 51], target: 17, just two numbers left.\n     |- Try 51 + 30 = 81. Evaluate 81 != 17, drop this branch.\n     |- Try 51 - 30 = 21. Evaluate 21 != 17, drop this branch.\n     |- Try 51 * 30 = 1530. Evaluate 1530 != 17, drop this branch.\n     |- Try 51 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 - 9 = 12. Add 12 to the number set. Current number set: [12, 51], target: 17, just two numbers left.\n     |- Try 51 + 12 = 63. Evaluate 63 != 17, drop this branch.\n     |- Try 51 - 12 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 51 * 12 = 612. Evaluate 612 != 17, drop this branch.\n     |- Try 51 \/ 12 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 21 * 9 = 189. Add 189 to the number set. Current number set: [189, 51], target: 17, just two numbers left.\n     |- Try 189 + 51 = 240. Evaluate 240 != 17, drop this branch.\n     |- Try 189 - 51 = 138. Evaluate 138 != 17, drop this branch.\n     |- Try 189 * 51 = 9639. 9639 exceeds the maximum intermediate result, drop this branch.\n     |- Try 189 \/ 51 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 21 \/ 9 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 28 - 23 = 5. Add 5 to the number set. Current number set: [5, 21, 9], target: 17. Options for choosing two numbers: [(5, 21), (5, 9), (21, 9)].\n   |- Pick two numbers (5, 21) (numbers left: [9]). Try possible operations.\n    |- Try 21 + 5 = 26. Add 26 to the number set. Current number set: [26, 9], target: 17, just two numbers left.\n     |- Try 26 + 9 = 35. Evaluate 35 != 17, drop this branch.\n     |- Try 26 - 9 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 - 9 = 17\nThe step before: 21 + 5 = 26\nThe first step: 28 - 23 = 5\n\nOutput the solution in the required format:\n<Solution>\n28 - 23 = 5\n21 + 5 = 26\n26 - 9 = 17\n<\/Solution>\n","item":{"nums":[23,28,21,9],"solution":["28 - 23 = 5","21 + 5 = 26","26 - 9 = 17"],"target":17}}
+{"instance_id":"countdown_2k_41","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [43, 20, 14, 34]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [43, 20, 14, 34], target: 25. Options for choosing two numbers: [(43, 20), (43, 14), (43, 34), (20, 14), (20, 34), (14, 34)].\n |- Pick two numbers (43, 20) (numbers left: [14, 34]). Try possible operations.\n  |- Try 43 + 20 = 63. Add 63 to the number set. Current number set: [63, 14, 34], target: 25. Options for choosing two numbers: [(63, 14), (63, 34), (14, 34)].\n   |- Pick two numbers (63, 14) (numbers left: [34]). Try possible operations.\n    |- Try 63 + 14 = 77. Add 77 to the number set. Current number set: [77, 34], target: 25, just two numbers left.\n     |- Try 77 + 34 = 111. Evaluate 111 != 25, drop this branch.\n     |- Try 77 - 34 = 43. Evaluate 43 != 25, drop this branch.\n     |- Try 77 * 34 = 2618. 2618 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 34 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 63 - 14 = 49. Add 49 to the number set. Current number set: [49, 34], target: 25, just two numbers left.\n     |- Try 49 + 34 = 83. Evaluate 83 != 25, drop this branch.\n     |- Try 49 - 34 = 15. Evaluate 15 != 25, drop this branch.\n     |- Try 49 * 34 = 1666. Evaluate 1666 != 25, drop this branch.\n     |- Try 49 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 63 * 14 = 882. Add 882 to the number set. Current number set: [882, 34], target: 25, just two numbers left.\n     |- Try 882 + 34 = 916. Evaluate 916 != 25, drop this branch.\n     |- Try 882 - 34 = 848. Evaluate 848 != 25, drop this branch.\n     |- Try 882 * 34 = 29988. 29988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 882 \/ 34 = 25.9. 25.9 is a decimal, drop this branch.\n    |- Try 63 \/ 14 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (63, 34) (numbers left: [14]). Try possible operations.\n    |- Try 63 + 34 = 97. Add 97 to the number set. Current number set: [97, 14], target: 25, just two numbers left.\n     |- Try 97 + 14 = 111. Evaluate 111 != 25, drop this branch.\n     |- Try 97 - 14 = 83. Evaluate 83 != 25, drop this branch.\n     |- Try 97 * 14 = 1358. Evaluate 1358 != 25, drop this branch.\n     |- Try 97 \/ 14 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 63 - 34 = 29. Add 29 to the number set. Current number set: [29, 14], target: 25, just two numbers left.\n     |- Try 29 + 14 = 43. Evaluate 43 != 25, drop this branch.\n     |- Try 29 - 14 = 15. Evaluate 15 != 25, drop this branch.\n     |- Try 29 * 14 = 406. Evaluate 406 != 25, drop this branch.\n     |- Try 29 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 63 * 34 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 34 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (14, 34) (numbers left: [63]). Try possible operations.\n    |- Try 34 + 14 = 48. Add 48 to the number set. Current number set: [48, 63], target: 25, just two numbers left.\n     |- Try 63 + 48 = 111. Evaluate 111 != 25, drop this branch.\n     |- Try 63 - 48 = 15. Evaluate 15 != 25, drop this branch.\n     |- Try 63 * 48 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 34 - 14 = 20. Add 20 to the number set. Current number set: [20, 63], target: 25, just two numbers left.\n     |- Try 63 + 20 = 83. Evaluate 83 != 25, drop this branch.\n     |- Try 63 - 20 = 43. Evaluate 43 != 25, drop this branch.\n     |- Try 63 * 20 = 1260. Evaluate 1260 != 25, drop this branch.\n     |- Try 63 \/ 20 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 34 * 14 = 476. Add 476 to the number set. Current number set: [476, 63], target: 25, just two numbers left.\n     |- Try 476 + 63 = 539. Evaluate 539 != 25, drop this branch.\n     |- Try 476 - 63 = 413. Evaluate 413 != 25, drop this branch.\n     |- Try 476 * 63 = 29988. 29988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 476 \/ 63 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 34 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 43 - 20 = 23. Add 23 to the number set. Current number set: [23, 14, 34], target: 25. Options for choosing two numbers: [(23, 14), (23, 34), (14, 34)].\n   |- Pick two numbers (23, 14) (numbers left: [34]). Try possible operations.\n    |- Try 23 + 14 = 37. Add 37 to the number set. Current number set: [37, 34], target: 25, just two numbers left.\n     |- Try 37 + 34 = 71. Evaluate 71 != 25, drop this branch.\n     |- Try 37 - 34 = 3. Evaluate 3 != 25, drop this branch.\n     |- Try 37 * 34 = 1258. Evaluate 1258 != 25, drop this branch.\n     |- Try 37 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 23 - 14 = 9. Add 9 to the number set. Current number set: [9, 34], target: 25, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 25, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 - 9 = 25\nThe step before: 23 - 14 = 9\nThe first step: 43 - 20 = 23\n\nOutput the solution in the required format:\n<Solution>\n43 - 20 = 23\n23 - 14 = 9\n34 - 9 = 25\n<\/Solution>\n","item":{"nums":[43,20,14,34],"solution":["43 - 20 = 23","23 - 14 = 9","34 - 9 = 25"],"target":25}}
+{"instance_id":"countdown_2k_42","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 30, 19, 20]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [5, 30, 19, 20], target: 35. Options for choosing two numbers: [(5, 30), (5, 19), (5, 20), (30, 19), (30, 20), (19, 20)].\n |- Pick two numbers (5, 30) (numbers left: [19, 20]). Try possible operations.\n  |- Try 30 + 5 = 35. Add 35 to the number set. Current number set: [35, 19, 20], target: 35. Options for choosing two numbers: [(35, 19), (35, 20), (19, 20)].\n   |- Pick two numbers (35, 19) (numbers left: [20]). Try possible operations.\n    |- Try 35 + 19 = 54. Add 54 to the number set. Current number set: [54, 20], target: 35, just two numbers left.\n     |- Try 54 + 20 = 74. Evaluate 74 != 35, drop this branch.\n     |- Try 54 - 20 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 54 * 20 = 1080. Evaluate 1080 != 35, drop this branch.\n     |- Try 54 \/ 20 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 35 - 19 = 16. Add 16 to the number set. Current number set: [16, 20], target: 35, just two numbers left.\n     |- Try 20 + 16 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 20 - 16 = 4. Evaluate 4 != 35, drop this branch.\n     |- Try 20 * 16 = 320. Evaluate 320 != 35, drop this branch.\n     |- Try 20 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 * 19 = 665. Add 665 to the number set. Current number set: [665, 20], target: 35, just two numbers left.\n     |- Try 665 + 20 = 685. Evaluate 685 != 35, drop this branch.\n     |- Try 665 - 20 = 645. Evaluate 645 != 35, drop this branch.\n     |- Try 665 * 20 = 13300. 13300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 665 \/ 20 = 33.2. 33.2 is a decimal, drop this branch.\n    |- Try 35 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (35, 20) (numbers left: [19]). Try possible operations.\n    |- Try 35 + 20 = 55. Add 55 to the number set. Current number set: [55, 19], target: 35, just two numbers left.\n     |- Try 55 + 19 = 74. Evaluate 74 != 35, drop this branch.\n     |- Try 55 - 19 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 55 * 19 = 1045. Evaluate 1045 != 35, drop this branch.\n     |- Try 55 \/ 19 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 35 - 20 = 15. Add 15 to the number set. Current number set: [15, 19], target: 35, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 35, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 35, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 * 20 = 700. Add 700 to the number set. Current number set: [700, 19], target: 35, just two numbers left.\n     |- Try 700 + 19 = 719. Evaluate 719 != 35, drop this branch.\n     |- Try 700 - 19 = 681. Evaluate 681 != 35, drop this branch.\n     |- Try 700 * 19 = 13300. 13300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 700 \/ 19 = 36.8. 36.8 is a decimal, drop this branch.\n    |- Try 35 \/ 20 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (19, 20) (numbers left: [35]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 35], target: 35, just two numbers left.\n     |- Try 39 + 35 = 74. Evaluate 74 != 35, drop this branch.\n     |- Try 39 - 35 = 4. Evaluate 4 != 35, drop this branch.\n     |- Try 39 * 35 = 1365. Evaluate 1365 != 35, drop this branch.\n     |- Try 39 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 35], target: 35, just two numbers left.\n     |- Try 35 + 1 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 35 - 1 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 35 * 1 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 * 1 = 35\nThe step before: 20 - 19 = 1\nThe first step: 30 + 5 = 35\n\nOutput the solution in the required format:\n<Solution>\n30 + 5 = 35\n20 - 19 = 1\n35 * 1 = 35\n<\/Solution>\n","item":{"nums":[5,30,19,20],"solution":["30 + 5 = 35","20 - 19 = 1","35 * 1 = 35"],"target":35}}
+{"instance_id":"countdown_2k_43","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 38, 32, 13]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [24, 38, 32, 13], target: 33. Options for choosing two numbers: [(24, 38), (24, 32), (24, 13), (38, 32), (38, 13), (32, 13)].\n |- Pick two numbers (24, 38) (numbers left: [32, 13]). Try possible operations.\n  |- Try 38 + 24 = 62. Add 62 to the number set. Current number set: [62, 32, 13], target: 33. Options for choosing two numbers: [(62, 32), (62, 13), (32, 13)].\n   |- Pick two numbers (62, 32) (numbers left: [13]). Try possible operations.\n    |- Try 62 + 32 = 94. Add 94 to the number set. Current number set: [94, 13], target: 33, just two numbers left.\n     |- Try 94 + 13 = 107. Evaluate 107 != 33, drop this branch.\n     |- Try 94 - 13 = 81. Evaluate 81 != 33, drop this branch.\n     |- Try 94 * 13 = 1222. Evaluate 1222 != 33, drop this branch.\n     |- Try 94 \/ 13 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 62 - 32 = 30. Add 30 to the number set. Current number set: [30, 13], target: 33, just two numbers left.\n     |- Try 30 + 13 = 43. Evaluate 43 != 33, drop this branch.\n     |- Try 30 - 13 = 17. Evaluate 17 != 33, drop this branch.\n     |- Try 30 * 13 = 390. Evaluate 390 != 33, drop this branch.\n     |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 62 * 32 = 1984. Add 1984 to the number set. Current number set: [1984, 13], target: 33, just two numbers left.\n     |- Try 1984 + 13 = 1997. Evaluate 1997 != 33, drop this branch.\n     |- Try 1984 - 13 = 1971. Evaluate 1971 != 33, drop this branch.\n     |- Try 1984 * 13 = 25792. 25792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1984 \/ 13 = 152.6. 152.6 is a decimal, drop this branch.\n    |- Try 62 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (62, 13) (numbers left: [32]). Try possible operations.\n    |- Try 62 + 13 = 75. Add 75 to the number set. Current number set: [75, 32], target: 33, just two numbers left.\n     |- Try 75 + 32 = 107. Evaluate 107 != 33, drop this branch.\n     |- Try 75 - 32 = 43. Evaluate 43 != 33, drop this branch.\n     |- Try 75 * 32 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 32 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 62 - 13 = 49. Add 49 to the number set. Current number set: [49, 32], target: 33, just two numbers left.\n     |- Try 49 + 32 = 81. Evaluate 81 != 33, drop this branch.\n     |- Try 49 - 32 = 17. Evaluate 17 != 33, drop this branch.\n     |- Try 49 * 32 = 1568. Evaluate 1568 != 33, drop this branch.\n     |- Try 49 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 62 * 13 = 806. Add 806 to the number set. Current number set: [806, 32], target: 33, just two numbers left.\n     |- Try 806 + 32 = 838. Evaluate 838 != 33, drop this branch.\n     |- Try 806 - 32 = 774. Evaluate 774 != 33, drop this branch.\n     |- Try 806 * 32 = 25792. 25792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 806 \/ 32 = 25.2. 25.2 is a decimal, drop this branch.\n    |- Try 62 \/ 13 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (32, 13) (numbers left: [62]). Try possible operations.\n    |- Try 32 + 13 = 45. Add 45 to the number set. Current number set: [45, 62], target: 33, just two numbers left.\n     |- Try 62 + 45 = 107. Evaluate 107 != 33, drop this branch.\n     |- Try 62 - 45 = 17. Evaluate 17 != 33, drop this branch.\n     |- Try 62 * 45 = 2790. 2790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 45 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 - 13 = 19. Add 19 to the number set. Current number set: [19, 62], target: 33, just two numbers left.\n     |- Try 62 + 19 = 81. Evaluate 81 != 33, drop this branch.\n     |- Try 62 - 19 = 43. Evaluate 43 != 33, drop this branch.\n     |- Try 62 * 19 = 1178. Evaluate 1178 != 33, drop this branch.\n     |- Try 62 \/ 19 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 32 * 13 = 416. Add 416 to the number set. Current number set: [416, 62], target: 33, just two numbers left.\n     |- Try 416 + 62 = 478. Evaluate 478 != 33, drop this branch.\n     |- Try 416 - 62 = 354. Evaluate 354 != 33, drop this branch.\n     |- Try 416 * 62 = 25792. 25792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 416 \/ 62 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 32 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 38 - 24 = 14. Add 14 to the number set. Current number set: [14, 32, 13], target: 33. Options for choosing two numbers: [(14, 32), (14, 13), (32, 13)].\n   |- Pick two numbers (14, 32) (numbers left: [13]). Try possible operations.\n    |- Try 32 + 14 = 46. Add 46 to the number set. Current number set: [46, 13], target: 33, just two numbers left.\n     |- Try 46 + 13 = 59. Evaluate 59 != 33, drop this branch.\n     |- Try 46 - 13 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 46 - 13 = 33\nThe step before: 32 + 14 = 46\nThe first step: 38 - 24 = 14\n\nOutput the solution in the required format:\n<Solution>\n38 - 24 = 14\n32 + 14 = 46\n46 - 13 = 33\n<\/Solution>\n","item":{"nums":[24,38,32,13],"solution":["38 - 24 = 14","32 + 14 = 46","46 - 13 = 33"],"target":33}}
+{"instance_id":"countdown_2k_44","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 16, 10, 1]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [49, 16, 10, 1], target: 44. Options for choosing two numbers: [(49, 16), (49, 10), (49, 1), (16, 10), (16, 1), (10, 1)].\n |- Pick two numbers (49, 16) (numbers left: [10, 1]). Try possible operations.\n  |- Try 49 + 16 = 65. Add 65 to the number set. Current number set: [65, 10, 1], target: 44. Options for choosing two numbers: [(65, 10), (65, 1), (10, 1)].\n   |- Pick two numbers (65, 10) (numbers left: [1]). Try possible operations.\n    |- Try 65 + 10 = 75. Add 75 to the number set. Current number set: [75, 1], target: 44, just two numbers left.\n     |- Try 75 + 1 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 75 - 1 = 74. Evaluate 74 != 44, drop this branch.\n     |- Try 75 * 1 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 75 \/ 1 = 75. Evaluate 75 != 44, drop this branch.\n    |- Try 65 - 10 = 55. Add 55 to the number set. Current number set: [55, 1], target: 44, just two numbers left.\n     |- Try 55 + 1 = 56. Evaluate 56 != 44, drop this branch.\n     |- Try 55 - 1 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 55 * 1 = 55. Evaluate 55 != 44, drop this branch.\n     |- Try 55 \/ 1 = 55. Evaluate 55 != 44, drop this branch.\n    |- Try 65 * 10 = 650. Add 650 to the number set. Current number set: [650, 1], target: 44, just two numbers left.\n     |- Try 650 + 1 = 651. Evaluate 651 != 44, drop this branch.\n     |- Try 650 - 1 = 649. Evaluate 649 != 44, drop this branch.\n     |- Try 650 * 1 = 650. Evaluate 650 != 44, drop this branch.\n     |- Try 650 \/ 1 = 650. Evaluate 650 != 44, drop this branch.\n    |- Try 65 \/ 10 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (65, 1) (numbers left: [10]). Try possible operations.\n    |- Try 65 + 1 = 66. Add 66 to the number set. Current number set: [66, 10], target: 44, just two numbers left.\n     |- Try 66 + 10 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 66 - 10 = 56. Evaluate 56 != 44, drop this branch.\n     |- Try 66 * 10 = 660. Evaluate 660 != 44, drop this branch.\n     |- Try 66 \/ 10 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 65 - 1 = 64. Add 64 to the number set. Current number set: [64, 10], target: 44, just two numbers left.\n     |- Try 64 + 10 = 74. Evaluate 74 != 44, drop this branch.\n     |- Try 64 - 10 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 64 * 10 = 640. Evaluate 640 != 44, drop this branch.\n     |- Try 64 \/ 10 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 65 * 1 = 65. Add 65 to the number set. Current number set: [65, 10], target: 44, just two numbers left.\n     |- Try 65 + 10 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 65 - 10 = 55. Evaluate 55 != 44, drop this branch.\n     |- Try 65 * 10 = 650. Evaluate 650 != 44, drop this branch.\n     |- Try 65 \/ 10 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 65 \/ 1 = 65. Add 65 to the number set. Current number set: [65, 10], target: 44, just two numbers left.\n     |- Try 65 + 10 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 65 - 10 = 55. Evaluate 55 != 44, drop this branch.\n     |- Try 65 * 10 = 650. Evaluate 650 != 44, drop this branch.\n     |- Try 65 \/ 10 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (10, 1) (numbers left: [65]). Try possible operations.\n    |- Try 10 + 1 = 11. Add 11 to the number set. Current number set: [11, 65], target: 44, just two numbers left.\n     |- Try 65 + 11 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 65 - 11 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 65 * 11 = 715. Evaluate 715 != 44, drop this branch.\n     |- Try 65 \/ 11 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 10 - 1 = 9. Add 9 to the number set. Current number set: [9, 65], target: 44, just two numbers left.\n     |- Try 65 + 9 = 74. Evaluate 74 != 44, drop this branch.\n     |- Try 65 - 9 = 56. Evaluate 56 != 44, drop this branch.\n     |- Try 65 * 9 = 585. Evaluate 585 != 44, drop this branch.\n     |- Try 65 \/ 9 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 10 * 1 = 10. Add 10 to the number set. Current number set: [10, 65], target: 44, just two numbers left.\n     |- Try 65 + 10 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 65 - 10 = 55. Evaluate 55 != 44, drop this branch.\n     |- Try 65 * 10 = 650. Evaluate 650 != 44, drop this branch.\n     |- Try 65 \/ 10 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 10 \/ 1 = 10. Add 10 to the number set. Current number set: [10, 65], target: 44, just two numbers left.\n     |- Try 65 + 10 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 65 - 10 = 55. Evaluate 55 != 44, drop this branch.\n     |- Try 65 * 10 = 650. Evaluate 650 != 44, drop this branch.\n     |- Try 65 \/ 10 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 49 - 16 = 33. Add 33 to the number set. Current number set: [33, 10, 1], target: 44. Options for choosing two numbers: [(33, 10), (33, 1), (10, 1)].\n   |- Pick two numbers (33, 10) (numbers left: [1]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 1], target: 44, just two numbers left.\n     |- Try 43 + 1 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 + 1 = 44\nThe step before: 33 + 10 = 43\nThe first step: 49 - 16 = 33\n\nOutput the solution in the required format:\n<Solution>\n49 - 16 = 33\n33 + 10 = 43\n43 + 1 = 44\n<\/Solution>\n","item":{"nums":[49,16,10,1],"solution":["49 - 16 = 33","33 + 10 = 43","43 + 1 = 44"],"target":44}}
+{"instance_id":"countdown_2k_45","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 48, 4, 49]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [35, 48, 4, 49], target: 32. Options for choosing two numbers: [(35, 48), (35, 4), (35, 49), (48, 4), (48, 49), (4, 49)].\n |- Pick two numbers (35, 48) (numbers left: [4, 49]). Try possible operations.\n  |- Try 48 + 35 = 83. Add 83 to the number set. Current number set: [83, 4, 49], target: 32. Options for choosing two numbers: [(83, 4), (83, 49), (4, 49)].\n   |- Pick two numbers (83, 4) (numbers left: [49]). Try possible operations.\n    |- Try 83 + 4 = 87. Add 87 to the number set. Current number set: [87, 49], target: 32, just two numbers left.\n     |- Try 87 + 49 = 136. Evaluate 136 != 32, drop this branch.\n     |- Try 87 - 49 = 38. Evaluate 38 != 32, drop this branch.\n     |- Try 87 * 49 = 4263. 4263 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 49 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 83 - 4 = 79. Add 79 to the number set. Current number set: [79, 49], target: 32, just two numbers left.\n     |- Try 79 + 49 = 128. Evaluate 128 != 32, drop this branch.\n     |- Try 79 - 49 = 30. Evaluate 30 != 32, drop this branch.\n     |- Try 79 * 49 = 3871. 3871 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 83 * 4 = 332. Add 332 to the number set. Current number set: [332, 49], target: 32, just two numbers left.\n     |- Try 332 + 49 = 381. Evaluate 381 != 32, drop this branch.\n     |- Try 332 - 49 = 283. Evaluate 283 != 32, drop this branch.\n     |- Try 332 * 49 = 16268. 16268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 332 \/ 49 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 83 \/ 4 = 20.8. 20.8 is a decimal, drop this branch.\n   |- Pick two numbers (83, 49) (numbers left: [4]). Try possible operations.\n    |- Try 83 + 49 = 132. Add 132 to the number set. Current number set: [132, 4], target: 32, just two numbers left.\n     |- Try 132 + 4 = 136. Evaluate 136 != 32, drop this branch.\n     |- Try 132 - 4 = 128. Evaluate 128 != 32, drop this branch.\n     |- Try 132 * 4 = 528. Evaluate 528 != 32, drop this branch.\n     |- Try 132 \/ 4 = 33. Evaluate 33 != 32, drop this branch.\n    |- Try 83 - 49 = 34. Add 34 to the number set. Current number set: [34, 4], target: 32, just two numbers left.\n     |- Try 34 + 4 = 38. Evaluate 38 != 32, drop this branch.\n     |- Try 34 - 4 = 30. Evaluate 30 != 32, drop this branch.\n     |- Try 34 * 4 = 136. Evaluate 136 != 32, drop this branch.\n     |- Try 34 \/ 4 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 83 * 49 = 4067. 4067 exceeds the maximum intermediate result, drop this branch.\n    |- Try 83 \/ 49 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (4, 49) (numbers left: [83]). Try possible operations.\n    |- Try 49 + 4 = 53. Add 53 to the number set. Current number set: [53, 83], target: 32, just two numbers left.\n     |- Try 83 + 53 = 136. Evaluate 136 != 32, drop this branch.\n     |- Try 83 - 53 = 30. Evaluate 30 != 32, drop this branch.\n     |- Try 83 * 53 = 4399. 4399 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 53 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 49 - 4 = 45. Add 45 to the number set. Current number set: [45, 83], target: 32, just two numbers left.\n     |- Try 83 + 45 = 128. Evaluate 128 != 32, drop this branch.\n     |- Try 83 - 45 = 38. Evaluate 38 != 32, drop this branch.\n     |- Try 83 * 45 = 3735. 3735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 49 * 4 = 196. Add 196 to the number set. Current number set: [196, 83], target: 32, just two numbers left.\n     |- Try 196 + 83 = 279. Evaluate 279 != 32, drop this branch.\n     |- Try 196 - 83 = 113. Evaluate 113 != 32, drop this branch.\n     |- Try 196 * 83 = 16268. 16268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 83 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n  |- Try 48 - 35 = 13. Add 13 to the number set. Current number set: [13, 4, 49], target: 32. Options for choosing two numbers: [(13, 4), (13, 49), (4, 49)].\n   |- Pick two numbers (13, 4) (numbers left: [49]). Try possible operations.\n    |- Try 13 + 4 = 17. Add 17 to the number set. Current number set: [17, 49], target: 32, just two numbers left.\n     |- Try 49 + 17 = 66. Evaluate 66 != 32, drop this branch.\n     |- Try 49 - 17 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 - 17 = 32\nThe step before: 13 + 4 = 17\nThe first step: 48 - 35 = 13\n\nOutput the solution in the required format:\n<Solution>\n48 - 35 = 13\n13 + 4 = 17\n49 - 17 = 32\n<\/Solution>\n","item":{"nums":[35,48,4,49],"solution":["48 - 35 = 13","13 + 4 = 17","49 - 17 = 32"],"target":32}}
+{"instance_id":"countdown_2k_46","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 32, 42, 21]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [41, 32, 42, 21], target: 30. Options for choosing two numbers: [(41, 32), (41, 42), (41, 21), (32, 42), (32, 21), (42, 21)].\n |- Pick two numbers (41, 32) (numbers left: [42, 21]). Try possible operations.\n  |- Try 41 + 32 = 73. Add 73 to the number set. Current number set: [73, 42, 21], target: 30. Options for choosing two numbers: [(73, 42), (73, 21), (42, 21)].\n   |- Pick two numbers (73, 42) (numbers left: [21]). Try possible operations.\n    |- Try 73 + 42 = 115. Add 115 to the number set. Current number set: [115, 21], target: 30, just two numbers left.\n     |- Try 115 + 21 = 136. Evaluate 136 != 30, drop this branch.\n     |- Try 115 - 21 = 94. Evaluate 94 != 30, drop this branch.\n     |- Try 115 * 21 = 2415. 2415 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 21 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 73 - 42 = 31. Add 31 to the number set. Current number set: [31, 21], target: 30, just two numbers left.\n     |- Try 31 + 21 = 52. Evaluate 52 != 30, drop this branch.\n     |- Try 31 - 21 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 31 * 21 = 651. Evaluate 651 != 30, drop this branch.\n     |- Try 31 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 73 * 42 = 3066. 3066 exceeds the maximum intermediate result, drop this branch.\n    |- Try 73 \/ 42 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (73, 21) (numbers left: [42]). Try possible operations.\n    |- Try 73 + 21 = 94. Add 94 to the number set. Current number set: [94, 42], target: 30, just two numbers left.\n     |- Try 94 + 42 = 136. Evaluate 136 != 30, drop this branch.\n     |- Try 94 - 42 = 52. Evaluate 52 != 30, drop this branch.\n     |- Try 94 * 42 = 3948. 3948 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 42 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 73 - 21 = 52. Add 52 to the number set. Current number set: [52, 42], target: 30, just two numbers left.\n     |- Try 52 + 42 = 94. Evaluate 94 != 30, drop this branch.\n     |- Try 52 - 42 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 52 * 42 = 2184. 2184 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 73 * 21 = 1533. Add 1533 to the number set. Current number set: [1533, 42], target: 30, just two numbers left.\n     |- Try 1533 + 42 = 1575. Evaluate 1575 != 30, drop this branch.\n     |- Try 1533 - 42 = 1491. Evaluate 1491 != 30, drop this branch.\n     |- Try 1533 * 42 = 64386. 64386 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1533 \/ 42 = 36.5. 36.5 is a decimal, drop this branch.\n    |- Try 73 \/ 21 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (42, 21) (numbers left: [73]). Try possible operations.\n    |- Try 42 + 21 = 63. Add 63 to the number set. Current number set: [63, 73], target: 30, just two numbers left.\n     |- Try 73 + 63 = 136. Evaluate 136 != 30, drop this branch.\n     |- Try 73 - 63 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 73 * 63 = 4599. 4599 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 63 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 - 21 = 21. Add 21 to the number set. Current number set: [21, 73], target: 30, just two numbers left.\n     |- Try 73 + 21 = 94. Evaluate 94 != 30, drop this branch.\n     |- Try 73 - 21 = 52. Evaluate 52 != 30, drop this branch.\n     |- Try 73 * 21 = 1533. Evaluate 1533 != 30, drop this branch.\n     |- Try 73 \/ 21 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 * 21 = 882. Add 882 to the number set. Current number set: [882, 73], target: 30, just two numbers left.\n     |- Try 882 + 73 = 955. Evaluate 955 != 30, drop this branch.\n     |- Try 882 - 73 = 809. Evaluate 809 != 30, drop this branch.\n     |- Try 882 * 73 = 64386. 64386 exceeds the maximum intermediate result, drop this branch.\n     |- Try 882 \/ 73 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 42 \/ 21 = 2. Add 2 to the number set. Current number set: [2, 73], target: 30, just two numbers left.\n     |- Try 73 + 2 = 75. Evaluate 75 != 30, drop this branch.\n     |- Try 73 - 2 = 71. Evaluate 71 != 30, drop this branch.\n     |- Try 73 * 2 = 146. Evaluate 146 != 30, drop this branch.\n     |- Try 73 \/ 2 = 36.5. 36.5 is a decimal, drop this branch.\n  |- Try 41 - 32 = 9. Add 9 to the number set. Current number set: [9, 42, 21], target: 30. Options for choosing two numbers: [(9, 42), (9, 21), (42, 21)].\n   |- Pick two numbers (9, 42) (numbers left: [21]). Try possible operations.\n    |- Try 42 + 9 = 51. Add 51 to the number set. Current number set: [51, 21], target: 30, just two numbers left.\n     |- Try 51 + 21 = 72. Evaluate 72 != 30, drop this branch.\n     |- Try 51 - 21 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 51 - 21 = 30\nThe step before: 42 + 9 = 51\nThe first step: 41 - 32 = 9\n\nOutput the solution in the required format:\n<Solution>\n41 - 32 = 9\n42 + 9 = 51\n51 - 21 = 30\n<\/Solution>\n","item":{"nums":[41,32,42,21],"solution":["41 - 32 = 9","42 + 9 = 51","51 - 21 = 30"],"target":30}}
+{"instance_id":"countdown_2k_47","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 27, 45, 36]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [13, 27, 45, 36], target: 23. Options for choosing two numbers: [(13, 27), (13, 45), (13, 36), (27, 45), (27, 36), (45, 36)].\n |- Pick two numbers (13, 27) (numbers left: [45, 36]). Try possible operations.\n  |- Try 27 + 13 = 40. Add 40 to the number set. Current number set: [40, 45, 36], target: 23. Options for choosing two numbers: [(40, 45), (40, 36), (45, 36)].\n   |- Pick two numbers (40, 45) (numbers left: [36]). Try possible operations.\n    |- Try 45 + 40 = 85. Add 85 to the number set. Current number set: [85, 36], target: 23, just two numbers left.\n     |- Try 85 + 36 = 121. Evaluate 121 != 23, drop this branch.\n     |- Try 85 - 36 = 49. Evaluate 49 != 23, drop this branch.\n     |- Try 85 * 36 = 3060. 3060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 36 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 45 - 40 = 5. Add 5 to the number set. Current number set: [5, 36], target: 23, just two numbers left.\n     |- Try 36 + 5 = 41. Evaluate 41 != 23, drop this branch.\n     |- Try 36 - 5 = 31. Evaluate 31 != 23, drop this branch.\n     |- Try 36 * 5 = 180. Evaluate 180 != 23, drop this branch.\n     |- Try 36 \/ 5 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 45 * 40 = 1800. Add 1800 to the number set. Current number set: [1800, 36], target: 23, just two numbers left.\n     |- Try 1800 + 36 = 1836. Evaluate 1836 != 23, drop this branch.\n     |- Try 1800 - 36 = 1764. Evaluate 1764 != 23, drop this branch.\n     |- Try 1800 * 36 = 64800. 64800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1800 \/ 36 = 50. Evaluate 50 != 23, drop this branch.\n    |- Try 45 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (40, 36) (numbers left: [45]). Try possible operations.\n    |- Try 40 + 36 = 76. Add 76 to the number set. Current number set: [76, 45], target: 23, just two numbers left.\n     |- Try 76 + 45 = 121. Evaluate 121 != 23, drop this branch.\n     |- Try 76 - 45 = 31. Evaluate 31 != 23, drop this branch.\n     |- Try 76 * 45 = 3420. 3420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 45 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 40 - 36 = 4. Add 4 to the number set. Current number set: [4, 45], target: 23, just two numbers left.\n     |- Try 45 + 4 = 49. Evaluate 49 != 23, drop this branch.\n     |- Try 45 - 4 = 41. Evaluate 41 != 23, drop this branch.\n     |- Try 45 * 4 = 180. Evaluate 180 != 23, drop this branch.\n     |- Try 45 \/ 4 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 40 * 36 = 1440. Add 1440 to the number set. Current number set: [1440, 45], target: 23, just two numbers left.\n     |- Try 1440 + 45 = 1485. Evaluate 1485 != 23, drop this branch.\n     |- Try 1440 - 45 = 1395. Evaluate 1395 != 23, drop this branch.\n     |- Try 1440 * 45 = 64800. 64800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1440 \/ 45 = 32. Evaluate 32 != 23, drop this branch.\n    |- Try 40 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (45, 36) (numbers left: [40]). Try possible operations.\n    |- Try 45 + 36 = 81. Add 81 to the number set. Current number set: [81, 40], target: 23, just two numbers left.\n     |- Try 81 + 40 = 121. Evaluate 121 != 23, drop this branch.\n     |- Try 81 - 40 = 41. Evaluate 41 != 23, drop this branch.\n     |- Try 81 * 40 = 3240. 3240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 40 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 45 - 36 = 9. Add 9 to the number set. Current number set: [9, 40], target: 23, just two numbers left.\n     |- Try 40 + 9 = 49. Evaluate 49 != 23, drop this branch.\n     |- Try 40 - 9 = 31. Evaluate 31 != 23, drop this branch.\n     |- Try 40 * 9 = 360. Evaluate 360 != 23, drop this branch.\n     |- Try 40 \/ 9 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 45 * 36 = 1620. Add 1620 to the number set. Current number set: [1620, 40], target: 23, just two numbers left.\n     |- Try 1620 + 40 = 1660. Evaluate 1660 != 23, drop this branch.\n     |- Try 1620 - 40 = 1580. Evaluate 1580 != 23, drop this branch.\n     |- Try 1620 * 40 = 64800. 64800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1620 \/ 40 = 40.5. 40.5 is a decimal, drop this branch.\n    |- Try 45 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 27 - 13 = 14. Add 14 to the number set. Current number set: [14, 45, 36], target: 23. Options for choosing two numbers: [(14, 45), (14, 36), (45, 36)].\n   |- Pick two numbers (14, 45) (numbers left: [36]). Try possible operations.\n    |- Try 45 + 14 = 59. Add 59 to the number set. Current number set: [59, 36], target: 23, just two numbers left.\n     |- Try 59 + 36 = 95. Evaluate 95 != 23, drop this branch.\n     |- Try 59 - 36 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 59 - 36 = 23\nThe step before: 45 + 14 = 59\nThe first step: 27 - 13 = 14\n\nOutput the solution in the required format:\n<Solution>\n27 - 13 = 14\n45 + 14 = 59\n59 - 36 = 23\n<\/Solution>\n","item":{"nums":[13,27,45,36],"solution":["27 - 13 = 14","45 + 14 = 59","59 - 36 = 23"],"target":23}}
+{"instance_id":"countdown_2k_48","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 33, 37, 34]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [3, 33, 37, 34], target: 12. Options for choosing two numbers: [(3, 33), (3, 37), (3, 34), (33, 37), (33, 34), (37, 34)].\n |- Pick two numbers (3, 33) (numbers left: [37, 34]). Try possible operations.\n  |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 37, 34], target: 12. Options for choosing two numbers: [(36, 37), (36, 34), (37, 34)].\n   |- Pick two numbers (36, 37) (numbers left: [34]). Try possible operations.\n    |- Try 37 + 36 = 73. Add 73 to the number set. Current number set: [73, 34], target: 12, just two numbers left.\n     |- Try 73 + 34 = 107. Evaluate 107 != 12, drop this branch.\n     |- Try 73 - 34 = 39. Evaluate 39 != 12, drop this branch.\n     |- Try 73 * 34 = 2482. 2482 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 34 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 37 - 36 = 1. Add 1 to the number set. Current number set: [1, 34], target: 12, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 12, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 12, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 12, drop this branch.\n    |- Try 37 * 36 = 1332. Add 1332 to the number set. Current number set: [1332, 34], target: 12, just two numbers left.\n     |- Try 1332 + 34 = 1366. Evaluate 1366 != 12, drop this branch.\n     |- Try 1332 - 34 = 1298. Evaluate 1298 != 12, drop this branch.\n     |- Try 1332 * 34 = 45288. 45288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1332 \/ 34 = 39.2. 39.2 is a decimal, drop this branch.\n    |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (36, 34) (numbers left: [37]). Try possible operations.\n    |- Try 36 + 34 = 70. Add 70 to the number set. Current number set: [70, 37], target: 12, just two numbers left.\n     |- Try 70 + 37 = 107. Evaluate 107 != 12, drop this branch.\n     |- Try 70 - 37 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 70 * 37 = 2590. 2590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 37 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 - 34 = 2. Add 2 to the number set. Current number set: [2, 37], target: 12, just two numbers left.\n     |- Try 37 + 2 = 39. Evaluate 39 != 12, drop this branch.\n     |- Try 37 - 2 = 35. Evaluate 35 != 12, drop this branch.\n     |- Try 37 * 2 = 74. Evaluate 74 != 12, drop this branch.\n     |- Try 37 \/ 2 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 36 * 34 = 1224. Add 1224 to the number set. Current number set: [1224, 37], target: 12, just two numbers left.\n     |- Try 1224 + 37 = 1261. Evaluate 1261 != 12, drop this branch.\n     |- Try 1224 - 37 = 1187. Evaluate 1187 != 12, drop this branch.\n     |- Try 1224 * 37 = 45288. 45288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1224 \/ 37 = 33.1. 33.1 is a decimal, drop this branch.\n    |- Try 36 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (37, 34) (numbers left: [36]). Try possible operations.\n    |- Try 37 + 34 = 71. Add 71 to the number set. Current number set: [71, 36], target: 12, just two numbers left.\n     |- Try 71 + 36 = 107. Evaluate 107 != 12, drop this branch.\n     |- Try 71 - 36 = 35. Evaluate 35 != 12, drop this branch.\n     |- Try 71 * 36 = 2556. 2556 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 36 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 37 - 34 = 3. Add 3 to the number set. Current number set: [3, 36], target: 12, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 12, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 36 * 3 = 108. Evaluate 108 != 12, drop this branch.\n     |- Try 36 \/ 3 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 \/ 3 = 12\nThe step before: 37 - 34 = 3\nThe first step: 33 + 3 = 36\n\nOutput the solution in the required format:\n<Solution>\n33 + 3 = 36\n37 - 34 = 3\n36 \/ 3 = 12\n<\/Solution>\n","item":{"nums":[3,33,37,34],"solution":["33 + 3 = 36","37 - 34 = 3","36 \/ 3 = 12"],"target":12}}
+{"instance_id":"countdown_2k_49","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [36, 21, 18, 34]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [36, 21, 18, 34], target: 37. Options for choosing two numbers: [(36, 21), (36, 18), (36, 34), (21, 18), (21, 34), (18, 34)].\n |- Pick two numbers (36, 21) (numbers left: [18, 34]). Try possible operations.\n  |- Try 36 + 21 = 57. Add 57 to the number set. Current number set: [57, 18, 34], target: 37. Options for choosing two numbers: [(57, 18), (57, 34), (18, 34)].\n   |- Pick two numbers (57, 18) (numbers left: [34]). Try possible operations.\n    |- Try 57 + 18 = 75. Add 75 to the number set. Current number set: [75, 34], target: 37, just two numbers left.\n     |- Try 75 + 34 = 109. Evaluate 109 != 37, drop this branch.\n     |- Try 75 - 34 = 41. Evaluate 41 != 37, drop this branch.\n     |- Try 75 * 34 = 2550. 2550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 34 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 57 - 18 = 39. Add 39 to the number set. Current number set: [39, 34], target: 37, just two numbers left.\n     |- Try 39 + 34 = 73. Evaluate 73 != 37, drop this branch.\n     |- Try 39 - 34 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 39 * 34 = 1326. Evaluate 1326 != 37, drop this branch.\n     |- Try 39 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 57 * 18 = 1026. Add 1026 to the number set. Current number set: [1026, 34], target: 37, just two numbers left.\n     |- Try 1026 + 34 = 1060. Evaluate 1060 != 37, drop this branch.\n     |- Try 1026 - 34 = 992. Evaluate 992 != 37, drop this branch.\n     |- Try 1026 * 34 = 34884. 34884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1026 \/ 34 = 30.2. 30.2 is a decimal, drop this branch.\n    |- Try 57 \/ 18 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (57, 34) (numbers left: [18]). Try possible operations.\n    |- Try 57 + 34 = 91. Add 91 to the number set. Current number set: [91, 18], target: 37, just two numbers left.\n     |- Try 91 + 18 = 109. Evaluate 109 != 37, drop this branch.\n     |- Try 91 - 18 = 73. Evaluate 73 != 37, drop this branch.\n     |- Try 91 * 18 = 1638. Evaluate 1638 != 37, drop this branch.\n     |- Try 91 \/ 18 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 57 - 34 = 23. Add 23 to the number set. Current number set: [23, 18], target: 37, just two numbers left.\n     |- Try 23 + 18 = 41. Evaluate 41 != 37, drop this branch.\n     |- Try 23 - 18 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 23 * 18 = 414. Evaluate 414 != 37, drop this branch.\n     |- Try 23 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 57 * 34 = 1938. Add 1938 to the number set. Current number set: [1938, 18], target: 37, just two numbers left.\n     |- Try 1938 + 18 = 1956. Evaluate 1956 != 37, drop this branch.\n     |- Try 1938 - 18 = 1920. Evaluate 1920 != 37, drop this branch.\n     |- Try 1938 * 18 = 34884. 34884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1938 \/ 18 = 107.7. 107.7 is a decimal, drop this branch.\n    |- Try 57 \/ 34 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (18, 34) (numbers left: [57]). Try possible operations.\n    |- Try 34 + 18 = 52. Add 52 to the number set. Current number set: [52, 57], target: 37, just two numbers left.\n     |- Try 57 + 52 = 109. Evaluate 109 != 37, drop this branch.\n     |- Try 57 - 52 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 57 * 52 = 2964. 2964 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 52 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 34 - 18 = 16. Add 16 to the number set. Current number set: [16, 57], target: 37, just two numbers left.\n     |- Try 57 + 16 = 73. Evaluate 73 != 37, drop this branch.\n     |- Try 57 - 16 = 41. Evaluate 41 != 37, drop this branch.\n     |- Try 57 * 16 = 912. Evaluate 912 != 37, drop this branch.\n     |- Try 57 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 34 * 18 = 612. Add 612 to the number set. Current number set: [612, 57], target: 37, just two numbers left.\n     |- Try 612 + 57 = 669. Evaluate 669 != 37, drop this branch.\n     |- Try 612 - 57 = 555. Evaluate 555 != 37, drop this branch.\n     |- Try 612 * 57 = 34884. 34884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 612 \/ 57 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 36 - 21 = 15. Add 15 to the number set. Current number set: [15, 18, 34], target: 37. Options for choosing two numbers: [(15, 18), (15, 34), (18, 34)].\n   |- Pick two numbers (15, 18) (numbers left: [34]). Try possible operations.\n    |- Try 18 + 15 = 33. Add 33 to the number set. Current number set: [33, 34], target: 37, just two numbers left.\n     |- Try 34 + 33 = 67. Evaluate 67 != 37, drop this branch.\n     |- Try 34 - 33 = 1. Evaluate 1 != 37, drop this branch.\n     |- Try 34 * 33 = 1122. Evaluate 1122 != 37, drop this branch.\n     |- Try 34 \/ 33 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 15 = 3. Add 3 to the number set. Current number set: [3, 34], target: 37, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 3 = 37\nThe step before: 18 - 15 = 3\nThe first step: 36 - 21 = 15\n\nOutput the solution in the required format:\n<Solution>\n36 - 21 = 15\n18 - 15 = 3\n34 + 3 = 37\n<\/Solution>\n","item":{"nums":[36,21,18,34],"solution":["36 - 21 = 15","18 - 15 = 3","34 + 3 = 37"],"target":37}}
+{"instance_id":"countdown_2k_50","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 19, 35, 23]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [7, 19, 35, 23], target: 46. Options for choosing two numbers: [(7, 19), (7, 35), (7, 23), (19, 35), (19, 23), (35, 23)].\n |- Pick two numbers (7, 19) (numbers left: [35, 23]). Try possible operations.\n  |- Try 19 + 7 = 26. Add 26 to the number set. Current number set: [26, 35, 23], target: 46. Options for choosing two numbers: [(26, 35), (26, 23), (35, 23)].\n   |- Pick two numbers (26, 35) (numbers left: [23]). Try possible operations.\n    |- Try 35 + 26 = 61. Add 61 to the number set. Current number set: [61, 23], target: 46, just two numbers left.\n     |- Try 61 + 23 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 61 - 23 = 38. Evaluate 38 != 46, drop this branch.\n     |- Try 61 * 23 = 1403. Evaluate 1403 != 46, drop this branch.\n     |- Try 61 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 35 - 26 = 9. Add 9 to the number set. Current number set: [9, 23], target: 46, just two numbers left.\n     |- Try 23 + 9 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 23 - 9 = 14. Evaluate 14 != 46, drop this branch.\n     |- Try 23 * 9 = 207. Evaluate 207 != 46, drop this branch.\n     |- Try 23 \/ 9 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 35 * 26 = 910. Add 910 to the number set. Current number set: [910, 23], target: 46, just two numbers left.\n     |- Try 910 + 23 = 933. Evaluate 933 != 46, drop this branch.\n     |- Try 910 - 23 = 887. Evaluate 887 != 46, drop this branch.\n     |- Try 910 * 23 = 20930. 20930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 910 \/ 23 = 39.6. 39.6 is a decimal, drop this branch.\n    |- Try 35 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (26, 23) (numbers left: [35]). Try possible operations.\n    |- Try 26 + 23 = 49. Add 49 to the number set. Current number set: [49, 35], target: 46, just two numbers left.\n     |- Try 49 + 35 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 49 - 35 = 14. Evaluate 14 != 46, drop this branch.\n     |- Try 49 * 35 = 1715. Evaluate 1715 != 46, drop this branch.\n     |- Try 49 \/ 35 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 26 - 23 = 3. Add 3 to the number set. Current number set: [3, 35], target: 46, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 != 46, drop this branch.\n     |- Try 35 - 3 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 35 * 3 = 105. Evaluate 105 != 46, drop this branch.\n     |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 26 * 23 = 598. Add 598 to the number set. Current number set: [598, 35], target: 46, just two numbers left.\n     |- Try 598 + 35 = 633. Evaluate 633 != 46, drop this branch.\n     |- Try 598 - 35 = 563. Evaluate 563 != 46, drop this branch.\n     |- Try 598 * 35 = 20930. 20930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 598 \/ 35 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 26 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (35, 23) (numbers left: [26]). Try possible operations.\n    |- Try 35 + 23 = 58. Add 58 to the number set. Current number set: [58, 26], target: 46, just two numbers left.\n     |- Try 58 + 26 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 58 - 26 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 58 * 26 = 1508. Evaluate 1508 != 46, drop this branch.\n     |- Try 58 \/ 26 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 35 - 23 = 12. Add 12 to the number set. Current number set: [12, 26], target: 46, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 46, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 46, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 46, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 35 * 23 = 805. Add 805 to the number set. Current number set: [805, 26], target: 46, just two numbers left.\n     |- Try 805 + 26 = 831. Evaluate 831 != 46, drop this branch.\n     |- Try 805 - 26 = 779. Evaluate 779 != 46, drop this branch.\n     |- Try 805 * 26 = 20930. 20930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 805 \/ 26 = 31.0. 31.0 is a decimal, drop this branch.\n    |- Try 35 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 19 - 7 = 12. Add 12 to the number set. Current number set: [12, 35, 23], target: 46. Options for choosing two numbers: [(12, 35), (12, 23), (35, 23)].\n   |- Pick two numbers (12, 35) (numbers left: [23]). Try possible operations.\n    |- Try 35 + 12 = 47. Add 47 to the number set. Current number set: [47, 23], target: 46, just two numbers left.\n     |- Try 47 + 23 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 47 - 23 = 24. Evaluate 24 != 46, drop this branch.\n     |- Try 47 * 23 = 1081. Evaluate 1081 != 46, drop this branch.\n     |- Try 47 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 35 - 12 = 23. Add 23 to the number set. Current number set: [23, 23], target: 46, just two numbers left.\n     |- Try 23 + 23 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 23 = 46\nThe step before: 35 - 12 = 23\nThe first step: 19 - 7 = 12\n\nOutput the solution in the required format:\n<Solution>\n19 - 7 = 12\n35 - 12 = 23\n23 + 23 = 46\n<\/Solution>\n","item":{"nums":[7,19,35,23],"solution":["19 - 7 = 12","35 - 12 = 23","23 + 23 = 46"],"target":46}}
+{"instance_id":"countdown_2k_51","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 39, 31, 3]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [37, 39, 31, 3], target: 36. Options for choosing two numbers: [(37, 39), (37, 31), (37, 3), (39, 31), (39, 3), (31, 3)].\n |- Pick two numbers (37, 39) (numbers left: [31, 3]). Try possible operations.\n  |- Try 39 + 37 = 76. Add 76 to the number set. Current number set: [76, 31, 3], target: 36. Options for choosing two numbers: [(76, 31), (76, 3), (31, 3)].\n   |- Pick two numbers (76, 31) (numbers left: [3]). Try possible operations.\n    |- Try 76 + 31 = 107. Add 107 to the number set. Current number set: [107, 3], target: 36, just two numbers left.\n     |- Try 107 + 3 = 110. Evaluate 110 != 36, drop this branch.\n     |- Try 107 - 3 = 104. Evaluate 104 != 36, drop this branch.\n     |- Try 107 * 3 = 321. Evaluate 321 != 36, drop this branch.\n     |- Try 107 \/ 3 = 35.7. 35.7 is a decimal, drop this branch.\n    |- Try 76 - 31 = 45. Add 45 to the number set. Current number set: [45, 3], target: 36, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 36, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 36, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 36, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 36, drop this branch.\n    |- Try 76 * 31 = 2356. 2356 exceeds the maximum intermediate result, drop this branch.\n    |- Try 76 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (76, 3) (numbers left: [31]). Try possible operations.\n    |- Try 76 + 3 = 79. Add 79 to the number set. Current number set: [79, 31], target: 36, just two numbers left.\n     |- Try 79 + 31 = 110. Evaluate 110 != 36, drop this branch.\n     |- Try 79 - 31 = 48. Evaluate 48 != 36, drop this branch.\n     |- Try 79 * 31 = 2449. 2449 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 76 - 3 = 73. Add 73 to the number set. Current number set: [73, 31], target: 36, just two numbers left.\n     |- Try 73 + 31 = 104. Evaluate 104 != 36, drop this branch.\n     |- Try 73 - 31 = 42. Evaluate 42 != 36, drop this branch.\n     |- Try 73 * 31 = 2263. 2263 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 31 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 76 * 3 = 228. Add 228 to the number set. Current number set: [228, 31], target: 36, just two numbers left.\n     |- Try 228 + 31 = 259. Evaluate 259 != 36, drop this branch.\n     |- Try 228 - 31 = 197. Evaluate 197 != 36, drop this branch.\n     |- Try 228 * 31 = 7068. 7068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 31 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 76 \/ 3 = 25.3. 25.3 is a decimal, drop this branch.\n   |- Pick two numbers (31, 3) (numbers left: [76]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 76], target: 36, just two numbers left.\n     |- Try 76 + 34 = 110. Evaluate 110 != 36, drop this branch.\n     |- Try 76 - 34 = 42. Evaluate 42 != 36, drop this branch.\n     |- Try 76 * 34 = 2584. 2584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 34 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 76], target: 36, just two numbers left.\n     |- Try 76 + 28 = 104. Evaluate 104 != 36, drop this branch.\n     |- Try 76 - 28 = 48. Evaluate 48 != 36, drop this branch.\n     |- Try 76 * 28 = 2128. 2128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 28 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 76], target: 36, just two numbers left.\n     |- Try 93 + 76 = 169. Evaluate 169 != 36, drop this branch.\n     |- Try 93 - 76 = 17. Evaluate 17 != 36, drop this branch.\n     |- Try 93 * 76 = 7068. 7068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 76 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 39 - 37 = 2. Add 2 to the number set. Current number set: [2, 31, 3], target: 36. Options for choosing two numbers: [(2, 31), (2, 3), (31, 3)].\n   |- Pick two numbers (2, 31) (numbers left: [3]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 3], target: 36, just two numbers left.\n     |- Try 33 + 3 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 + 3 = 36\nThe step before: 31 + 2 = 33\nThe first step: 39 - 37 = 2\n\nOutput the solution in the required format:\n<Solution>\n39 - 37 = 2\n31 + 2 = 33\n33 + 3 = 36\n<\/Solution>\n","item":{"nums":[37,39,31,3],"solution":["39 - 37 = 2","31 + 2 = 33","33 + 3 = 36"],"target":36}}
+{"instance_id":"countdown_2k_52","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 32, 45, 44]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [18, 32, 45, 44], target: 13. Options for choosing two numbers: [(18, 32), (18, 45), (18, 44), (32, 45), (32, 44), (45, 44)].\n |- Pick two numbers (18, 32) (numbers left: [45, 44]). Try possible operations.\n  |- Try 32 + 18 = 50. Add 50 to the number set. Current number set: [50, 45, 44], target: 13. Options for choosing two numbers: [(50, 45), (50, 44), (45, 44)].\n   |- Pick two numbers (50, 45) (numbers left: [44]). Try possible operations.\n    |- Try 50 + 45 = 95. Add 95 to the number set. Current number set: [95, 44], target: 13, just two numbers left.\n     |- Try 95 + 44 = 139. Evaluate 139 != 13, drop this branch.\n     |- Try 95 - 44 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 95 * 44 = 4180. 4180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 44 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 50 - 45 = 5. Add 5 to the number set. Current number set: [5, 44], target: 13, just two numbers left.\n     |- Try 44 + 5 = 49. Evaluate 49 != 13, drop this branch.\n     |- Try 44 - 5 = 39. Evaluate 39 != 13, drop this branch.\n     |- Try 44 * 5 = 220. Evaluate 220 != 13, drop this branch.\n     |- Try 44 \/ 5 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 50 * 45 = 2250. 2250 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (50, 44) (numbers left: [45]). Try possible operations.\n    |- Try 50 + 44 = 94. Add 94 to the number set. Current number set: [94, 45], target: 13, just two numbers left.\n     |- Try 94 + 45 = 139. Evaluate 139 != 13, drop this branch.\n     |- Try 94 - 45 = 49. Evaluate 49 != 13, drop this branch.\n     |- Try 94 * 45 = 4230. 4230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 45 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 50 - 44 = 6. Add 6 to the number set. Current number set: [6, 45], target: 13, just two numbers left.\n     |- Try 45 + 6 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 45 - 6 = 39. Evaluate 39 != 13, drop this branch.\n     |- Try 45 * 6 = 270. Evaluate 270 != 13, drop this branch.\n     |- Try 45 \/ 6 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 50 * 44 = 2200. 2200 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (45, 44) (numbers left: [50]). Try possible operations.\n    |- Try 45 + 44 = 89. Add 89 to the number set. Current number set: [89, 50], target: 13, just two numbers left.\n     |- Try 89 + 50 = 139. Evaluate 139 != 13, drop this branch.\n     |- Try 89 - 50 = 39. Evaluate 39 != 13, drop this branch.\n     |- Try 89 * 50 = 4450. 4450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 89 \/ 50 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 - 44 = 1. Add 1 to the number set. Current number set: [1, 50], target: 13, just two numbers left.\n     |- Try 50 + 1 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 50 - 1 = 49. Evaluate 49 != 13, drop this branch.\n     |- Try 50 * 1 = 50. Evaluate 50 != 13, drop this branch.\n     |- Try 50 \/ 1 = 50. Evaluate 50 != 13, drop this branch.\n    |- Try 45 * 44 = 1980. Add 1980 to the number set. Current number set: [1980, 50], target: 13, just two numbers left.\n     |- Try 1980 + 50 = 2030. 2030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 - 50 = 1930. Evaluate 1930 != 13, drop this branch.\n     |- Try 1980 * 50 = 99000. 99000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 \/ 50 = 39.6. 39.6 is a decimal, drop this branch.\n    |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 32 - 18 = 14. Add 14 to the number set. Current number set: [14, 45, 44], target: 13. Options for choosing two numbers: [(14, 45), (14, 44), (45, 44)].\n   |- Pick two numbers (14, 45) (numbers left: [44]). Try possible operations.\n    |- Try 45 + 14 = 59. Add 59 to the number set. Current number set: [59, 44], target: 13, just two numbers left.\n     |- Try 59 + 44 = 103. Evaluate 103 != 13, drop this branch.\n     |- Try 59 - 44 = 15. Evaluate 15 != 13, drop this branch.\n     |- Try 59 * 44 = 2596. 2596 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 44 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 45 - 14 = 31. Add 31 to the number set. Current number set: [31, 44], target: 13, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 13, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 31 = 13\nThe step before: 45 - 14 = 31\nThe first step: 32 - 18 = 14\n\nOutput the solution in the required format:\n<Solution>\n32 - 18 = 14\n45 - 14 = 31\n44 - 31 = 13\n<\/Solution>\n","item":{"nums":[18,32,45,44],"solution":["32 - 18 = 14","45 - 14 = 31","44 - 31 = 13"],"target":13}}
+{"instance_id":"countdown_2k_53","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 34, 37, 2]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [9, 34, 37, 2], target: 14. Options for choosing two numbers: [(9, 34), (9, 37), (9, 2), (34, 37), (34, 2), (37, 2)].\n |- Pick two numbers (9, 34) (numbers left: [37, 2]). Try possible operations.\n  |- Try 34 + 9 = 43. Add 43 to the number set. Current number set: [43, 37, 2], target: 14. Options for choosing two numbers: [(43, 37), (43, 2), (37, 2)].\n   |- Pick two numbers (43, 37) (numbers left: [2]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 2], target: 14, just two numbers left.\n     |- Try 80 + 2 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 80 - 2 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 80 * 2 = 160. Evaluate 160 != 14, drop this branch.\n     |- Try 80 \/ 2 = 40. Evaluate 40 != 14, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 2], target: 14, just two numbers left.\n     |- Try 6 + 2 = 8. Evaluate 8 != 14, drop this branch.\n     |- Try 6 - 2 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 6 * 2 = 12. Evaluate 12 != 14, drop this branch.\n     |- Try 6 \/ 2 = 3. Evaluate 3 != 14, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 2], target: 14, just two numbers left.\n     |- Try 1591 + 2 = 1593. Evaluate 1593 != 14, drop this branch.\n     |- Try 1591 - 2 = 1589. Evaluate 1589 != 14, drop this branch.\n     |- Try 1591 * 2 = 3182. 3182 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 2 = 795.5. 795.5 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (43, 2) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 2 = 45. Add 45 to the number set. Current number set: [45, 37], target: 14, just two numbers left.\n     |- Try 45 + 37 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 45 - 37 = 8. Evaluate 8 != 14, drop this branch.\n     |- Try 45 * 37 = 1665. Evaluate 1665 != 14, drop this branch.\n     |- Try 45 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 - 2 = 41. Add 41 to the number set. Current number set: [41, 37], target: 14, just two numbers left.\n     |- Try 41 + 37 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 41 - 37 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 41 * 37 = 1517. Evaluate 1517 != 14, drop this branch.\n     |- Try 41 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 2 = 86. Add 86 to the number set. Current number set: [86, 37], target: 14, just two numbers left.\n     |- Try 86 + 37 = 123. Evaluate 123 != 14, drop this branch.\n     |- Try 86 - 37 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 86 * 37 = 3182. 3182 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 37 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 43 \/ 2 = 21.5. 21.5 is a decimal, drop this branch.\n   |- Pick two numbers (37, 2) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 2 = 39. Add 39 to the number set. Current number set: [39, 43], target: 14, just two numbers left.\n     |- Try 43 + 39 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 43 - 39 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 43 * 39 = 1677. Evaluate 1677 != 14, drop this branch.\n     |- Try 43 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 2 = 35. Add 35 to the number set. Current number set: [35, 43], target: 14, just two numbers left.\n     |- Try 43 + 35 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 43 - 35 = 8. Evaluate 8 != 14, drop this branch.\n     |- Try 43 * 35 = 1505. Evaluate 1505 != 14, drop this branch.\n     |- Try 43 \/ 35 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 * 2 = 74. Add 74 to the number set. Current number set: [74, 43], target: 14, just two numbers left.\n     |- Try 74 + 43 = 117. Evaluate 117 != 14, drop this branch.\n     |- Try 74 - 43 = 31. Evaluate 31 != 14, drop this branch.\n     |- Try 74 * 43 = 3182. 3182 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 43 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 37 \/ 2 = 18.5. 18.5 is a decimal, drop this branch.\n  |- Try 34 - 9 = 25. Add 25 to the number set. Current number set: [25, 37, 2], target: 14. Options for choosing two numbers: [(25, 37), (25, 2), (37, 2)].\n   |- Pick two numbers (25, 37) (numbers left: [2]). Try possible operations.\n    |- Try 37 + 25 = 62. Add 62 to the number set. Current number set: [62, 2], target: 14, just two numbers left.\n     |- Try 62 + 2 = 64. Evaluate 64 != 14, drop this branch.\n     |- Try 62 - 2 = 60. Evaluate 60 != 14, drop this branch.\n     |- Try 62 * 2 = 124. Evaluate 124 != 14, drop this branch.\n     |- Try 62 \/ 2 = 31. Evaluate 31 != 14, drop this branch.\n    |- Try 37 - 25 = 12. Add 12 to the number set. Current number set: [12, 2], target: 14, just two numbers left.\n     |- Try 12 + 2 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 12 + 2 = 14\nThe step before: 37 - 25 = 12\nThe first step: 34 - 9 = 25\n\nOutput the solution in the required format:\n<Solution>\n34 - 9 = 25\n37 - 25 = 12\n12 + 2 = 14\n<\/Solution>\n","item":{"nums":[9,34,37,2],"solution":["34 - 9 = 25","37 - 25 = 12","12 + 2 = 14"],"target":14}}
+{"instance_id":"countdown_2k_54","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 22, 18, 41]\nTarget: 40","reference_output":"# Search Procedure\nInitial number set: [5, 22, 18, 41], target: 40. Options for choosing two numbers: [(5, 22), (5, 18), (5, 41), (22, 18), (22, 41), (18, 41)].\n |- Pick two numbers (5, 22) (numbers left: [18, 41]). Try possible operations.\n  |- Try 22 + 5 = 27. Add 27 to the number set. Current number set: [27, 18, 41], target: 40. Options for choosing two numbers: [(27, 18), (27, 41), (18, 41)].\n   |- Pick two numbers (27, 18) (numbers left: [41]). Try possible operations.\n    |- Try 27 + 18 = 45. Add 45 to the number set. Current number set: [45, 41], target: 40, just two numbers left.\n     |- Try 45 + 41 = 86. Evaluate 86 != 40, drop this branch.\n     |- Try 45 - 41 = 4. Evaluate 4 != 40, drop this branch.\n     |- Try 45 * 41 = 1845. Evaluate 1845 != 40, drop this branch.\n     |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 18 = 9. Add 9 to the number set. Current number set: [9, 41], target: 40, just two numbers left.\n     |- Try 41 + 9 = 50. Evaluate 50 != 40, drop this branch.\n     |- Try 41 - 9 = 32. Evaluate 32 != 40, drop this branch.\n     |- Try 41 * 9 = 369. Evaluate 369 != 40, drop this branch.\n     |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 27 * 18 = 486. Add 486 to the number set. Current number set: [486, 41], target: 40, just two numbers left.\n     |- Try 486 + 41 = 527. Evaluate 527 != 40, drop this branch.\n     |- Try 486 - 41 = 445. Evaluate 445 != 40, drop this branch.\n     |- Try 486 * 41 = 19926. 19926 exceeds the maximum intermediate result, drop this branch.\n     |- Try 486 \/ 41 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (27, 41) (numbers left: [18]). Try possible operations.\n    |- Try 41 + 27 = 68. Add 68 to the number set. Current number set: [68, 18], target: 40, just two numbers left.\n     |- Try 68 + 18 = 86. Evaluate 86 != 40, drop this branch.\n     |- Try 68 - 18 = 50. Evaluate 50 != 40, drop this branch.\n     |- Try 68 * 18 = 1224. Evaluate 1224 != 40, drop this branch.\n     |- Try 68 \/ 18 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 41 - 27 = 14. Add 14 to the number set. Current number set: [14, 18], target: 40, just two numbers left.\n     |- Try 18 + 14 = 32. Evaluate 32 != 40, drop this branch.\n     |- Try 18 - 14 = 4. Evaluate 4 != 40, drop this branch.\n     |- Try 18 * 14 = 252. Evaluate 252 != 40, drop this branch.\n     |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 * 27 = 1107. Add 1107 to the number set. Current number set: [1107, 18], target: 40, just two numbers left.\n     |- Try 1107 + 18 = 1125. Evaluate 1125 != 40, drop this branch.\n     |- Try 1107 - 18 = 1089. Evaluate 1089 != 40, drop this branch.\n     |- Try 1107 * 18 = 19926. 19926 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1107 \/ 18 = 61.5. 61.5 is a decimal, drop this branch.\n    |- Try 41 \/ 27 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 41) (numbers left: [27]). Try possible operations.\n    |- Try 41 + 18 = 59. Add 59 to the number set. Current number set: [59, 27], target: 40, just two numbers left.\n     |- Try 59 + 27 = 86. Evaluate 86 != 40, drop this branch.\n     |- Try 59 - 27 = 32. Evaluate 32 != 40, drop this branch.\n     |- Try 59 * 27 = 1593. Evaluate 1593 != 40, drop this branch.\n     |- Try 59 \/ 27 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 41 - 18 = 23. Add 23 to the number set. Current number set: [23, 27], target: 40, just two numbers left.\n     |- Try 27 + 23 = 50. Evaluate 50 != 40, drop this branch.\n     |- Try 27 - 23 = 4. Evaluate 4 != 40, drop this branch.\n     |- Try 27 * 23 = 621. Evaluate 621 != 40, drop this branch.\n     |- Try 27 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 18 = 738. Add 738 to the number set. Current number set: [738, 27], target: 40, just two numbers left.\n     |- Try 738 + 27 = 765. Evaluate 765 != 40, drop this branch.\n     |- Try 738 - 27 = 711. Evaluate 711 != 40, drop this branch.\n     |- Try 738 * 27 = 19926. 19926 exceeds the maximum intermediate result, drop this branch.\n     |- Try 738 \/ 27 = 27.3. 27.3 is a decimal, drop this branch.\n    |- Try 41 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 22 - 5 = 17. Add 17 to the number set. Current number set: [17, 18, 41], target: 40. Options for choosing two numbers: [(17, 18), (17, 41), (18, 41)].\n   |- Pick two numbers (17, 18) (numbers left: [41]). Try possible operations.\n    |- Try 18 + 17 = 35. Add 35 to the number set. Current number set: [35, 41], target: 40, just two numbers left.\n     |- Try 41 + 35 = 76. Evaluate 76 != 40, drop this branch.\n     |- Try 41 - 35 = 6. Evaluate 6 != 40, drop this branch.\n     |- Try 41 * 35 = 1435. Evaluate 1435 != 40, drop this branch.\n     |- Try 41 \/ 35 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 18 - 17 = 1. Add 1 to the number set. Current number set: [1, 41], target: 40, just two numbers left.\n     |- Try 41 + 1 = 42. Evaluate 42 != 40, drop this branch.\n     |- Try 41 - 1 = 40. Evaluate 40 == 40, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 - 1 = 40\nThe step before: 18 - 17 = 1\nThe first step: 22 - 5 = 17\n\nOutput the solution in the required format:\n<Solution>\n22 - 5 = 17\n18 - 17 = 1\n41 - 1 = 40\n<\/Solution>\n","item":{"nums":[5,22,18,41],"solution":["22 - 5 = 17","18 - 17 = 1","41 - 1 = 40"],"target":40}}
+{"instance_id":"countdown_2k_55","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [25, 33, 38, 20]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [25, 33, 38, 20], target: 50. Options for choosing two numbers: [(25, 33), (25, 38), (25, 20), (33, 38), (33, 20), (38, 20)].\n |- Pick two numbers (25, 33) (numbers left: [38, 20]). Try possible operations.\n  |- Try 33 + 25 = 58. Add 58 to the number set. Current number set: [58, 38, 20], target: 50. Options for choosing two numbers: [(58, 38), (58, 20), (38, 20)].\n   |- Pick two numbers (58, 38) (numbers left: [20]). Try possible operations.\n    |- Try 58 + 38 = 96. Add 96 to the number set. Current number set: [96, 20], target: 50, just two numbers left.\n     |- Try 96 + 20 = 116. Evaluate 116 != 50, drop this branch.\n     |- Try 96 - 20 = 76. Evaluate 76 != 50, drop this branch.\n     |- Try 96 * 20 = 1920. Evaluate 1920 != 50, drop this branch.\n     |- Try 96 \/ 20 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 58 - 38 = 20. Add 20 to the number set. Current number set: [20, 20], target: 50, just two numbers left.\n     |- Try 20 + 20 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 20 - 20 = 0. Evaluate 0 != 50, drop this branch.\n     |- Try 20 * 20 = 400. Evaluate 400 != 50, drop this branch.\n     |- Try 20 \/ 20 = 1. Evaluate 1 != 50, drop this branch.\n    |- Try 58 * 38 = 2204. 2204 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 38 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (58, 20) (numbers left: [38]). Try possible operations.\n    |- Try 58 + 20 = 78. Add 78 to the number set. Current number set: [78, 38], target: 50, just two numbers left.\n     |- Try 78 + 38 = 116. Evaluate 116 != 50, drop this branch.\n     |- Try 78 - 38 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 78 * 38 = 2964. 2964 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 38 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 58 - 20 = 38. Add 38 to the number set. Current number set: [38, 38], target: 50, just two numbers left.\n     |- Try 38 + 38 = 76. Evaluate 76 != 50, drop this branch.\n     |- Try 38 - 38 = 0. Evaluate 0 != 50, drop this branch.\n     |- Try 38 * 38 = 1444. Evaluate 1444 != 50, drop this branch.\n     |- Try 38 \/ 38 = 1. Evaluate 1 != 50, drop this branch.\n    |- Try 58 * 20 = 1160. Add 1160 to the number set. Current number set: [1160, 38], target: 50, just two numbers left.\n     |- Try 1160 + 38 = 1198. Evaluate 1198 != 50, drop this branch.\n     |- Try 1160 - 38 = 1122. Evaluate 1122 != 50, drop this branch.\n     |- Try 1160 * 38 = 44080. 44080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1160 \/ 38 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 58 \/ 20 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (38, 20) (numbers left: [58]). Try possible operations.\n    |- Try 38 + 20 = 58. Add 58 to the number set. Current number set: [58, 58], target: 50, just two numbers left.\n     |- Try 58 + 58 = 116. Evaluate 116 != 50, drop this branch.\n     |- Try 58 - 58 = 0. Evaluate 0 != 50, drop this branch.\n     |- Try 58 * 58 = 3364. 3364 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 58 = 1. Evaluate 1 != 50, drop this branch.\n    |- Try 38 - 20 = 18. Add 18 to the number set. Current number set: [18, 58], target: 50, just two numbers left.\n     |- Try 58 + 18 = 76. Evaluate 76 != 50, drop this branch.\n     |- Try 58 - 18 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 58 * 18 = 1044. Evaluate 1044 != 50, drop this branch.\n     |- Try 58 \/ 18 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 38 * 20 = 760. Add 760 to the number set. Current number set: [760, 58], target: 50, just two numbers left.\n     |- Try 760 + 58 = 818. Evaluate 818 != 50, drop this branch.\n     |- Try 760 - 58 = 702. Evaluate 702 != 50, drop this branch.\n     |- Try 760 * 58 = 44080. 44080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 58 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 38 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 33 - 25 = 8. Add 8 to the number set. Current number set: [8, 38, 20], target: 50. Options for choosing two numbers: [(8, 38), (8, 20), (38, 20)].\n   |- Pick two numbers (8, 38) (numbers left: [20]). Try possible operations.\n    |- Try 38 + 8 = 46. Add 46 to the number set. Current number set: [46, 20], target: 50, just two numbers left.\n     |- Try 46 + 20 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 46 - 20 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 46 * 20 = 920. Evaluate 920 != 50, drop this branch.\n     |- Try 46 \/ 20 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 38 - 8 = 30. Add 30 to the number set. Current number set: [30, 20], target: 50, just two numbers left.\n     |- Try 30 + 20 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 + 20 = 50\nThe step before: 38 - 8 = 30\nThe first step: 33 - 25 = 8\n\nOutput the solution in the required format:\n<Solution>\n33 - 25 = 8\n38 - 8 = 30\n30 + 20 = 50\n<\/Solution>\n","item":{"nums":[25,33,38,20],"solution":["33 - 25 = 8","38 - 8 = 30","30 + 20 = 50"],"target":50}}
+{"instance_id":"countdown_2k_56","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 24, 46, 42]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [8, 24, 46, 42], target: 20. Options for choosing two numbers: [(8, 24), (8, 46), (8, 42), (24, 46), (24, 42), (46, 42)].\n |- Pick two numbers (8, 24) (numbers left: [46, 42]). Try possible operations.\n  |- Try 24 + 8 = 32. Add 32 to the number set. Current number set: [32, 46, 42], target: 20. Options for choosing two numbers: [(32, 46), (32, 42), (46, 42)].\n   |- Pick two numbers (32, 46) (numbers left: [42]). Try possible operations.\n    |- Try 46 + 32 = 78. Add 78 to the number set. Current number set: [78, 42], target: 20, just two numbers left.\n     |- Try 78 + 42 = 120. Evaluate 120 != 20, drop this branch.\n     |- Try 78 - 42 = 36. Evaluate 36 != 20, drop this branch.\n     |- Try 78 * 42 = 3276. 3276 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 42 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 46 - 32 = 14. Add 14 to the number set. Current number set: [14, 42], target: 20, just two numbers left.\n     |- Try 42 + 14 = 56. Evaluate 56 != 20, drop this branch.\n     |- Try 42 - 14 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 42 * 14 = 588. Evaluate 588 != 20, drop this branch.\n     |- Try 42 \/ 14 = 3. Evaluate 3 != 20, drop this branch.\n    |- Try 46 * 32 = 1472. Add 1472 to the number set. Current number set: [1472, 42], target: 20, just two numbers left.\n     |- Try 1472 + 42 = 1514. Evaluate 1514 != 20, drop this branch.\n     |- Try 1472 - 42 = 1430. Evaluate 1430 != 20, drop this branch.\n     |- Try 1472 * 42 = 61824. 61824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1472 \/ 42 = 35.0. 35.0 is a decimal, drop this branch.\n    |- Try 46 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (32, 42) (numbers left: [46]). Try possible operations.\n    |- Try 42 + 32 = 74. Add 74 to the number set. Current number set: [74, 46], target: 20, just two numbers left.\n     |- Try 74 + 46 = 120. Evaluate 120 != 20, drop this branch.\n     |- Try 74 - 46 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 74 * 46 = 3404. 3404 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 46 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 42 - 32 = 10. Add 10 to the number set. Current number set: [10, 46], target: 20, just two numbers left.\n     |- Try 46 + 10 = 56. Evaluate 56 != 20, drop this branch.\n     |- Try 46 - 10 = 36. Evaluate 36 != 20, drop this branch.\n     |- Try 46 * 10 = 460. Evaluate 460 != 20, drop this branch.\n     |- Try 46 \/ 10 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 42 * 32 = 1344. Add 1344 to the number set. Current number set: [1344, 46], target: 20, just two numbers left.\n     |- Try 1344 + 46 = 1390. Evaluate 1390 != 20, drop this branch.\n     |- Try 1344 - 46 = 1298. Evaluate 1298 != 20, drop this branch.\n     |- Try 1344 * 46 = 61824. 61824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1344 \/ 46 = 29.2. 29.2 is a decimal, drop this branch.\n    |- Try 42 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (46, 42) (numbers left: [32]). Try possible operations.\n    |- Try 46 + 42 = 88. Add 88 to the number set. Current number set: [88, 32], target: 20, just two numbers left.\n     |- Try 88 + 32 = 120. Evaluate 120 != 20, drop this branch.\n     |- Try 88 - 32 = 56. Evaluate 56 != 20, drop this branch.\n     |- Try 88 * 32 = 2816. 2816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 32 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 46 - 42 = 4. Add 4 to the number set. Current number set: [4, 32], target: 20, just two numbers left.\n     |- Try 32 + 4 = 36. Evaluate 36 != 20, drop this branch.\n     |- Try 32 - 4 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 32 * 4 = 128. Evaluate 128 != 20, drop this branch.\n     |- Try 32 \/ 4 = 8. Evaluate 8 != 20, drop this branch.\n    |- Try 46 * 42 = 1932. Add 1932 to the number set. Current number set: [1932, 32], target: 20, just two numbers left.\n     |- Try 1932 + 32 = 1964. Evaluate 1964 != 20, drop this branch.\n     |- Try 1932 - 32 = 1900. Evaluate 1900 != 20, drop this branch.\n     |- Try 1932 * 32 = 61824. 61824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1932 \/ 32 = 60.4. 60.4 is a decimal, drop this branch.\n    |- Try 46 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 24 - 8 = 16. Add 16 to the number set. Current number set: [16, 46, 42], target: 20. Options for choosing two numbers: [(16, 46), (16, 42), (46, 42)].\n   |- Pick two numbers (16, 46) (numbers left: [42]). Try possible operations.\n    |- Try 46 + 16 = 62. Add 62 to the number set. Current number set: [62, 42], target: 20, just two numbers left.\n     |- Try 62 + 42 = 104. Evaluate 104 != 20, drop this branch.\n     |- Try 62 - 42 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 62 - 42 = 20\nThe step before: 46 + 16 = 62\nThe first step: 24 - 8 = 16\n\nOutput the solution in the required format:\n<Solution>\n24 - 8 = 16\n46 + 16 = 62\n62 - 42 = 20\n<\/Solution>\n","item":{"nums":[8,24,46,42],"solution":["24 - 8 = 16","46 + 16 = 62","62 - 42 = 20"],"target":20}}
+{"instance_id":"countdown_2k_57","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [45, 31, 22, 16]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [45, 31, 22, 16], target: 20. Options for choosing two numbers: [(45, 31), (45, 22), (45, 16), (31, 22), (31, 16), (22, 16)].\n |- Pick two numbers (45, 31) (numbers left: [22, 16]). Try possible operations.\n  |- Try 45 + 31 = 76. Add 76 to the number set. Current number set: [76, 22, 16], target: 20. Options for choosing two numbers: [(76, 22), (76, 16), (22, 16)].\n   |- Pick two numbers (76, 22) (numbers left: [16]). Try possible operations.\n    |- Try 76 + 22 = 98. Add 98 to the number set. Current number set: [98, 16], target: 20, just two numbers left.\n     |- Try 98 + 16 = 114. Evaluate 114 != 20, drop this branch.\n     |- Try 98 - 16 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 98 * 16 = 1568. Evaluate 1568 != 20, drop this branch.\n     |- Try 98 \/ 16 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 76 - 22 = 54. Add 54 to the number set. Current number set: [54, 16], target: 20, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 20, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 20, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 76 * 22 = 1672. Add 1672 to the number set. Current number set: [1672, 16], target: 20, just two numbers left.\n     |- Try 1672 + 16 = 1688. Evaluate 1688 != 20, drop this branch.\n     |- Try 1672 - 16 = 1656. Evaluate 1656 != 20, drop this branch.\n     |- Try 1672 * 16 = 26752. 26752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1672 \/ 16 = 104.5. 104.5 is a decimal, drop this branch.\n    |- Try 76 \/ 22 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (76, 16) (numbers left: [22]). Try possible operations.\n    |- Try 76 + 16 = 92. Add 92 to the number set. Current number set: [92, 22], target: 20, just two numbers left.\n     |- Try 92 + 22 = 114. Evaluate 114 != 20, drop this branch.\n     |- Try 92 - 22 = 70. Evaluate 70 != 20, drop this branch.\n     |- Try 92 * 22 = 2024. 2024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 22 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 76 - 16 = 60. Add 60 to the number set. Current number set: [60, 22], target: 20, just two numbers left.\n     |- Try 60 + 22 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 60 - 22 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 60 * 22 = 1320. Evaluate 1320 != 20, drop this branch.\n     |- Try 60 \/ 22 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 76 * 16 = 1216. Add 1216 to the number set. Current number set: [1216, 22], target: 20, just two numbers left.\n     |- Try 1216 + 22 = 1238. Evaluate 1238 != 20, drop this branch.\n     |- Try 1216 - 22 = 1194. Evaluate 1194 != 20, drop this branch.\n     |- Try 1216 * 22 = 26752. 26752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1216 \/ 22 = 55.3. 55.3 is a decimal, drop this branch.\n    |- Try 76 \/ 16 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (22, 16) (numbers left: [76]). Try possible operations.\n    |- Try 22 + 16 = 38. Add 38 to the number set. Current number set: [38, 76], target: 20, just two numbers left.\n     |- Try 76 + 38 = 114. Evaluate 114 != 20, drop this branch.\n     |- Try 76 - 38 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 76 * 38 = 2888. 2888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 38 = 2. Evaluate 2 != 20, drop this branch.\n    |- Try 22 - 16 = 6. Add 6 to the number set. Current number set: [6, 76], target: 20, just two numbers left.\n     |- Try 76 + 6 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 76 - 6 = 70. Evaluate 70 != 20, drop this branch.\n     |- Try 76 * 6 = 456. Evaluate 456 != 20, drop this branch.\n     |- Try 76 \/ 6 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 22 * 16 = 352. Add 352 to the number set. Current number set: [352, 76], target: 20, just two numbers left.\n     |- Try 352 + 76 = 428. Evaluate 428 != 20, drop this branch.\n     |- Try 352 - 76 = 276. Evaluate 276 != 20, drop this branch.\n     |- Try 352 * 76 = 26752. 26752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 76 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 45 - 31 = 14. Add 14 to the number set. Current number set: [14, 22, 16], target: 20. Options for choosing two numbers: [(14, 22), (14, 16), (22, 16)].\n   |- Pick two numbers (14, 22) (numbers left: [16]). Try possible operations.\n    |- Try 22 + 14 = 36. Add 36 to the number set. Current number set: [36, 16], target: 20, just two numbers left.\n     |- Try 36 + 16 = 52. Evaluate 52 != 20, drop this branch.\n     |- Try 36 - 16 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 16 = 20\nThe step before: 22 + 14 = 36\nThe first step: 45 - 31 = 14\n\nOutput the solution in the required format:\n<Solution>\n45 - 31 = 14\n22 + 14 = 36\n36 - 16 = 20\n<\/Solution>\n","item":{"nums":[45,31,22,16],"solution":["45 - 31 = 14","22 + 14 = 36","36 - 16 = 20"],"target":20}}
+{"instance_id":"countdown_2k_58","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 21, 1, 46]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [42, 21, 1, 46], target: 26. Options for choosing two numbers: [(42, 21), (42, 1), (42, 46), (21, 1), (21, 46), (1, 46)].\n |- Pick two numbers (42, 21) (numbers left: [1, 46]). Try possible operations.\n  |- Try 42 + 21 = 63. Add 63 to the number set. Current number set: [63, 1, 46], target: 26. Options for choosing two numbers: [(63, 1), (63, 46), (1, 46)].\n   |- Pick two numbers (63, 1) (numbers left: [46]). Try possible operations.\n    |- Try 63 + 1 = 64. Add 64 to the number set. Current number set: [64, 46], target: 26, just two numbers left.\n     |- Try 64 + 46 = 110. Evaluate 110 != 26, drop this branch.\n     |- Try 64 - 46 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 64 * 46 = 2944. 2944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 63 - 1 = 62. Add 62 to the number set. Current number set: [62, 46], target: 26, just two numbers left.\n     |- Try 62 + 46 = 108. Evaluate 108 != 26, drop this branch.\n     |- Try 62 - 46 = 16. Evaluate 16 != 26, drop this branch.\n     |- Try 62 * 46 = 2852. 2852 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 46 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 63 * 1 = 63. Add 63 to the number set. Current number set: [63, 46], target: 26, just two numbers left.\n     |- Try 63 + 46 = 109. Evaluate 109 != 26, drop this branch.\n     |- Try 63 - 46 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 63 * 46 = 2898. 2898 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 63 \/ 1 = 63. Add 63 to the number set. Current number set: [63, 46], target: 26, just two numbers left.\n     |- Try 63 + 46 = 109. Evaluate 109 != 26, drop this branch.\n     |- Try 63 - 46 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 63 * 46 = 2898. 2898 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (63, 46) (numbers left: [1]). Try possible operations.\n    |- Try 63 + 46 = 109. Add 109 to the number set. Current number set: [109, 1], target: 26, just two numbers left.\n     |- Try 109 + 1 = 110. Evaluate 110 != 26, drop this branch.\n     |- Try 109 - 1 = 108. Evaluate 108 != 26, drop this branch.\n     |- Try 109 * 1 = 109. Evaluate 109 != 26, drop this branch.\n     |- Try 109 \/ 1 = 109. Evaluate 109 != 26, drop this branch.\n    |- Try 63 - 46 = 17. Add 17 to the number set. Current number set: [17, 1], target: 26, just two numbers left.\n     |- Try 17 + 1 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 17 - 1 = 16. Evaluate 16 != 26, drop this branch.\n     |- Try 17 * 1 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 17 \/ 1 = 17. Evaluate 17 != 26, drop this branch.\n    |- Try 63 * 46 = 2898. 2898 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (1, 46) (numbers left: [63]). Try possible operations.\n    |- Try 46 + 1 = 47. Add 47 to the number set. Current number set: [47, 63], target: 26, just two numbers left.\n     |- Try 63 + 47 = 110. Evaluate 110 != 26, drop this branch.\n     |- Try 63 - 47 = 16. Evaluate 16 != 26, drop this branch.\n     |- Try 63 * 47 = 2961. 2961 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 47 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 46 - 1 = 45. Add 45 to the number set. Current number set: [45, 63], target: 26, just two numbers left.\n     |- Try 63 + 45 = 108. Evaluate 108 != 26, drop this branch.\n     |- Try 63 - 45 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 63 * 45 = 2835. 2835 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 45 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 * 1 = 46. Add 46 to the number set. Current number set: [46, 63], target: 26, just two numbers left.\n     |- Try 63 + 46 = 109. Evaluate 109 != 26, drop this branch.\n     |- Try 63 - 46 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 63 * 46 = 2898. 2898 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 \/ 1 = 46. Add 46 to the number set. Current number set: [46, 63], target: 26, just two numbers left.\n     |- Try 63 + 46 = 109. Evaluate 109 != 26, drop this branch.\n     |- Try 63 - 46 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 63 * 46 = 2898. 2898 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 42 - 21 = 21. Add 21 to the number set. Current number set: [21, 1, 46], target: 26. Options for choosing two numbers: [(21, 1), (21, 46), (1, 46)].\n   |- Pick two numbers (21, 1) (numbers left: [46]). Try possible operations.\n    |- Try 21 + 1 = 22. Add 22 to the number set. Current number set: [22, 46], target: 26, just two numbers left.\n     |- Try 46 + 22 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 46 - 22 = 24. Evaluate 24 != 26, drop this branch.\n     |- Try 46 * 22 = 1012. Evaluate 1012 != 26, drop this branch.\n     |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 21 - 1 = 20. Add 20 to the number set. Current number set: [20, 46], target: 26, just two numbers left.\n     |- Try 46 + 20 = 66. Evaluate 66 != 26, drop this branch.\n     |- Try 46 - 20 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 46 - 20 = 26\nThe step before: 21 - 1 = 20\nThe first step: 42 - 21 = 21\n\nOutput the solution in the required format:\n<Solution>\n42 - 21 = 21\n21 - 1 = 20\n46 - 20 = 26\n<\/Solution>\n","item":{"nums":[42,21,1,46],"solution":["42 - 21 = 21","21 - 1 = 20","46 - 20 = 26"],"target":26}}
+{"instance_id":"countdown_2k_59","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [28, 43, 47, 16]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [28, 43, 47, 16], target: 16. Options for choosing two numbers: [(28, 43), (28, 47), (28, 16), (43, 47), (43, 16), (47, 16)].\n |- Pick two numbers (28, 43) (numbers left: [47, 16]). Try possible operations.\n  |- Try 43 + 28 = 71. Add 71 to the number set. Current number set: [71, 47, 16], target: 16. Options for choosing two numbers: [(71, 47), (71, 16), (47, 16)].\n   |- Pick two numbers (71, 47) (numbers left: [16]). Try possible operations.\n    |- Try 71 + 47 = 118. Add 118 to the number set. Current number set: [118, 16], target: 16, just two numbers left.\n     |- Try 118 + 16 = 134. Evaluate 134 != 16, drop this branch.\n     |- Try 118 - 16 = 102. Evaluate 102 != 16, drop this branch.\n     |- Try 118 * 16 = 1888. Evaluate 1888 != 16, drop this branch.\n     |- Try 118 \/ 16 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 71 - 47 = 24. Add 24 to the number set. Current number set: [24, 16], target: 16, just two numbers left.\n     |- Try 24 + 16 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 24 - 16 = 8. Evaluate 8 != 16, drop this branch.\n     |- Try 24 * 16 = 384. Evaluate 384 != 16, drop this branch.\n     |- Try 24 \/ 16 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 71 * 47 = 3337. 3337 exceeds the maximum intermediate result, drop this branch.\n    |- Try 71 \/ 47 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (71, 16) (numbers left: [47]). Try possible operations.\n    |- Try 71 + 16 = 87. Add 87 to the number set. Current number set: [87, 47], target: 16, just two numbers left.\n     |- Try 87 + 47 = 134. Evaluate 134 != 16, drop this branch.\n     |- Try 87 - 47 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 87 * 47 = 4089. 4089 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 47 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 71 - 16 = 55. Add 55 to the number set. Current number set: [55, 47], target: 16, just two numbers left.\n     |- Try 55 + 47 = 102. Evaluate 102 != 16, drop this branch.\n     |- Try 55 - 47 = 8. Evaluate 8 != 16, drop this branch.\n     |- Try 55 * 47 = 2585. 2585 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 71 * 16 = 1136. Add 1136 to the number set. Current number set: [1136, 47], target: 16, just two numbers left.\n     |- Try 1136 + 47 = 1183. Evaluate 1183 != 16, drop this branch.\n     |- Try 1136 - 47 = 1089. Evaluate 1089 != 16, drop this branch.\n     |- Try 1136 * 47 = 53392. 53392 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1136 \/ 47 = 24.2. 24.2 is a decimal, drop this branch.\n    |- Try 71 \/ 16 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (47, 16) (numbers left: [71]). Try possible operations.\n    |- Try 47 + 16 = 63. Add 63 to the number set. Current number set: [63, 71], target: 16, just two numbers left.\n     |- Try 71 + 63 = 134. Evaluate 134 != 16, drop this branch.\n     |- Try 71 - 63 = 8. Evaluate 8 != 16, drop this branch.\n     |- Try 71 * 63 = 4473. 4473 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 63 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 47 - 16 = 31. Add 31 to the number set. Current number set: [31, 71], target: 16, just two numbers left.\n     |- Try 71 + 31 = 102. Evaluate 102 != 16, drop this branch.\n     |- Try 71 - 31 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 71 * 31 = 2201. 2201 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 31 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 47 * 16 = 752. Add 752 to the number set. Current number set: [752, 71], target: 16, just two numbers left.\n     |- Try 752 + 71 = 823. Evaluate 823 != 16, drop this branch.\n     |- Try 752 - 71 = 681. Evaluate 681 != 16, drop this branch.\n     |- Try 752 * 71 = 53392. 53392 exceeds the maximum intermediate result, drop this branch.\n     |- Try 752 \/ 71 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 47 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 43 - 28 = 15. Add 15 to the number set. Current number set: [15, 47, 16], target: 16. Options for choosing two numbers: [(15, 47), (15, 16), (47, 16)].\n   |- Pick two numbers (15, 47) (numbers left: [16]). Try possible operations.\n    |- Try 47 + 15 = 62. Add 62 to the number set. Current number set: [62, 16], target: 16, just two numbers left.\n     |- Try 62 + 16 = 78. Evaluate 78 != 16, drop this branch.\n     |- Try 62 - 16 = 46. Evaluate 46 != 16, drop this branch.\n     |- Try 62 * 16 = 992. Evaluate 992 != 16, drop this branch.\n     |- Try 62 \/ 16 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 47 - 15 = 32. Add 32 to the number set. Current number set: [32, 16], target: 16, just two numbers left.\n     |- Try 32 + 16 = 48. Evaluate 48 != 16, drop this branch.\n     |- Try 32 - 16 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 - 16 = 16\nThe step before: 47 - 15 = 32\nThe first step: 43 - 28 = 15\n\nOutput the solution in the required format:\n<Solution>\n43 - 28 = 15\n47 - 15 = 32\n32 - 16 = 16\n<\/Solution>\n","item":{"nums":[28,43,47,16],"solution":["43 - 28 = 15","47 - 15 = 32","32 - 16 = 16"],"target":16}}
+{"instance_id":"countdown_2k_60","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 48, 47, 27]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [46, 48, 47, 27], target: 18. Options for choosing two numbers: [(46, 48), (46, 47), (46, 27), (48, 47), (48, 27), (47, 27)].\n |- Pick two numbers (46, 48) (numbers left: [47, 27]). Try possible operations.\n  |- Try 48 + 46 = 94. Add 94 to the number set. Current number set: [94, 47, 27], target: 18. Options for choosing two numbers: [(94, 47), (94, 27), (47, 27)].\n   |- Pick two numbers (94, 47) (numbers left: [27]). Try possible operations.\n    |- Try 94 + 47 = 141. Add 141 to the number set. Current number set: [141, 27], target: 18, just two numbers left.\n     |- Try 141 + 27 = 168. Evaluate 168 != 18, drop this branch.\n     |- Try 141 - 27 = 114. Evaluate 114 != 18, drop this branch.\n     |- Try 141 * 27 = 3807. 3807 exceeds the maximum intermediate result, drop this branch.\n     |- Try 141 \/ 27 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 94 - 47 = 47. Add 47 to the number set. Current number set: [47, 27], target: 18, just two numbers left.\n     |- Try 47 + 27 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 47 - 27 = 20. Evaluate 20 != 18, drop this branch.\n     |- Try 47 * 27 = 1269. Evaluate 1269 != 18, drop this branch.\n     |- Try 47 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 94 * 47 = 4418. 4418 exceeds the maximum intermediate result, drop this branch.\n    |- Try 94 \/ 47 = 2. Add 2 to the number set. Current number set: [2, 27], target: 18, just two numbers left.\n     |- Try 27 + 2 = 29. Evaluate 29 != 18, drop this branch.\n     |- Try 27 - 2 = 25. Evaluate 25 != 18, drop this branch.\n     |- Try 27 * 2 = 54. Evaluate 54 != 18, drop this branch.\n     |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (94, 27) (numbers left: [47]). Try possible operations.\n    |- Try 94 + 27 = 121. Add 121 to the number set. Current number set: [121, 47], target: 18, just two numbers left.\n     |- Try 121 + 47 = 168. Evaluate 168 != 18, drop this branch.\n     |- Try 121 - 47 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 121 * 47 = 5687. 5687 exceeds the maximum intermediate result, drop this branch.\n     |- Try 121 \/ 47 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 94 - 27 = 67. Add 67 to the number set. Current number set: [67, 47], target: 18, just two numbers left.\n     |- Try 67 + 47 = 114. Evaluate 114 != 18, drop this branch.\n     |- Try 67 - 47 = 20. Evaluate 20 != 18, drop this branch.\n     |- Try 67 * 47 = 3149. 3149 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 47 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 94 * 27 = 2538. 2538 exceeds the maximum intermediate result, drop this branch.\n    |- Try 94 \/ 27 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (47, 27) (numbers left: [94]). Try possible operations.\n    |- Try 47 + 27 = 74. Add 74 to the number set. Current number set: [74, 94], target: 18, just two numbers left.\n     |- Try 94 + 74 = 168. Evaluate 168 != 18, drop this branch.\n     |- Try 94 - 74 = 20. Evaluate 20 != 18, drop this branch.\n     |- Try 94 * 74 = 6956. 6956 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 74 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 47 - 27 = 20. Add 20 to the number set. Current number set: [20, 94], target: 18, just two numbers left.\n     |- Try 94 + 20 = 114. Evaluate 114 != 18, drop this branch.\n     |- Try 94 - 20 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 94 * 20 = 1880. Evaluate 1880 != 18, drop this branch.\n     |- Try 94 \/ 20 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 47 * 27 = 1269. Add 1269 to the number set. Current number set: [1269, 94], target: 18, just two numbers left.\n     |- Try 1269 + 94 = 1363. Evaluate 1363 != 18, drop this branch.\n     |- Try 1269 - 94 = 1175. Evaluate 1175 != 18, drop this branch.\n     |- Try 1269 * 94 = 119286. 119286 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1269 \/ 94 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 47 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 48 - 46 = 2. Add 2 to the number set. Current number set: [2, 47, 27], target: 18. Options for choosing two numbers: [(2, 47), (2, 27), (47, 27)].\n   |- Pick two numbers (2, 47) (numbers left: [27]). Try possible operations.\n    |- Try 47 + 2 = 49. Add 49 to the number set. Current number set: [49, 27], target: 18, just two numbers left.\n     |- Try 49 + 27 = 76. Evaluate 76 != 18, drop this branch.\n     |- Try 49 - 27 = 22. Evaluate 22 != 18, drop this branch.\n     |- Try 49 * 27 = 1323. Evaluate 1323 != 18, drop this branch.\n     |- Try 49 \/ 27 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 47 - 2 = 45. Add 45 to the number set. Current number set: [45, 27], target: 18, just two numbers left.\n     |- Try 45 + 27 = 72. Evaluate 72 != 18, drop this branch.\n     |- Try 45 - 27 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 45 - 27 = 18\nThe step before: 47 - 2 = 45\nThe first step: 48 - 46 = 2\n\nOutput the solution in the required format:\n<Solution>\n48 - 46 = 2\n47 - 2 = 45\n45 - 27 = 18\n<\/Solution>\n","item":{"nums":[46,48,47,27],"solution":["48 - 46 = 2","47 - 2 = 45","45 - 27 = 18"],"target":18}}
+{"instance_id":"countdown_2k_61","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 35, 19, 28]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [48, 35, 19, 28], target: 22. Options for choosing two numbers: [(48, 35), (48, 19), (48, 28), (35, 19), (35, 28), (19, 28)].\n |- Pick two numbers (48, 35) (numbers left: [19, 28]). Try possible operations.\n  |- Try 48 + 35 = 83. Add 83 to the number set. Current number set: [83, 19, 28], target: 22. Options for choosing two numbers: [(83, 19), (83, 28), (19, 28)].\n   |- Pick two numbers (83, 19) (numbers left: [28]). Try possible operations.\n    |- Try 83 + 19 = 102. Add 102 to the number set. Current number set: [102, 28], target: 22, just two numbers left.\n     |- Try 102 + 28 = 130. Evaluate 130 != 22, drop this branch.\n     |- Try 102 - 28 = 74. Evaluate 74 != 22, drop this branch.\n     |- Try 102 * 28 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 28 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 83 - 19 = 64. Add 64 to the number set. Current number set: [64, 28], target: 22, just two numbers left.\n     |- Try 64 + 28 = 92. Evaluate 92 != 22, drop this branch.\n     |- Try 64 - 28 = 36. Evaluate 36 != 22, drop this branch.\n     |- Try 64 * 28 = 1792. Evaluate 1792 != 22, drop this branch.\n     |- Try 64 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 83 * 19 = 1577. Add 1577 to the number set. Current number set: [1577, 28], target: 22, just two numbers left.\n     |- Try 1577 + 28 = 1605. Evaluate 1605 != 22, drop this branch.\n     |- Try 1577 - 28 = 1549. Evaluate 1549 != 22, drop this branch.\n     |- Try 1577 * 28 = 44156. 44156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1577 \/ 28 = 56.3. 56.3 is a decimal, drop this branch.\n    |- Try 83 \/ 19 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (83, 28) (numbers left: [19]). Try possible operations.\n    |- Try 83 + 28 = 111. Add 111 to the number set. Current number set: [111, 19], target: 22, just two numbers left.\n     |- Try 111 + 19 = 130. Evaluate 130 != 22, drop this branch.\n     |- Try 111 - 19 = 92. Evaluate 92 != 22, drop this branch.\n     |- Try 111 * 19 = 2109. 2109 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 19 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 83 - 28 = 55. Add 55 to the number set. Current number set: [55, 19], target: 22, just two numbers left.\n     |- Try 55 + 19 = 74. Evaluate 74 != 22, drop this branch.\n     |- Try 55 - 19 = 36. Evaluate 36 != 22, drop this branch.\n     |- Try 55 * 19 = 1045. Evaluate 1045 != 22, drop this branch.\n     |- Try 55 \/ 19 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 83 * 28 = 2324. 2324 exceeds the maximum intermediate result, drop this branch.\n    |- Try 83 \/ 28 = 3.0. 3.0 is a decimal, drop this branch.\n   |- Pick two numbers (19, 28) (numbers left: [83]). Try possible operations.\n    |- Try 28 + 19 = 47. Add 47 to the number set. Current number set: [47, 83], target: 22, just two numbers left.\n     |- Try 83 + 47 = 130. Evaluate 130 != 22, drop this branch.\n     |- Try 83 - 47 = 36. Evaluate 36 != 22, drop this branch.\n     |- Try 83 * 47 = 3901. 3901 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 47 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 28 - 19 = 9. Add 9 to the number set. Current number set: [9, 83], target: 22, just two numbers left.\n     |- Try 83 + 9 = 92. Evaluate 92 != 22, drop this branch.\n     |- Try 83 - 9 = 74. Evaluate 74 != 22, drop this branch.\n     |- Try 83 * 9 = 747. Evaluate 747 != 22, drop this branch.\n     |- Try 83 \/ 9 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 28 * 19 = 532. Add 532 to the number set. Current number set: [532, 83], target: 22, just two numbers left.\n     |- Try 532 + 83 = 615. Evaluate 615 != 22, drop this branch.\n     |- Try 532 - 83 = 449. Evaluate 449 != 22, drop this branch.\n     |- Try 532 * 83 = 44156. 44156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 532 \/ 83 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 48 - 35 = 13. Add 13 to the number set. Current number set: [13, 19, 28], target: 22. Options for choosing two numbers: [(13, 19), (13, 28), (19, 28)].\n   |- Pick two numbers (13, 19) (numbers left: [28]). Try possible operations.\n    |- Try 19 + 13 = 32. Add 32 to the number set. Current number set: [32, 28], target: 22, just two numbers left.\n     |- Try 32 + 28 = 60. Evaluate 60 != 22, drop this branch.\n     |- Try 32 - 28 = 4. Evaluate 4 != 22, drop this branch.\n     |- Try 32 * 28 = 896. Evaluate 896 != 22, drop this branch.\n     |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 19 - 13 = 6. Add 6 to the number set. Current number set: [6, 28], target: 22, just two numbers left.\n     |- Try 28 + 6 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 28 - 6 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 - 6 = 22\nThe step before: 19 - 13 = 6\nThe first step: 48 - 35 = 13\n\nOutput the solution in the required format:\n<Solution>\n48 - 35 = 13\n19 - 13 = 6\n28 - 6 = 22\n<\/Solution>\n","item":{"nums":[48,35,19,28],"solution":["48 - 35 = 13","19 - 13 = 6","28 - 6 = 22"],"target":22}}
+{"instance_id":"countdown_2k_62","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 29, 12, 44]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [19, 29, 12, 44], target: 22. Options for choosing two numbers: [(19, 29), (19, 12), (19, 44), (29, 12), (29, 44), (12, 44)].\n |- Pick two numbers (19, 29) (numbers left: [12, 44]). Try possible operations.\n  |- Try 29 + 19 = 48. Add 48 to the number set. Current number set: [48, 12, 44], target: 22. Options for choosing two numbers: [(48, 12), (48, 44), (12, 44)].\n   |- Pick two numbers (48, 12) (numbers left: [44]). Try possible operations.\n    |- Try 48 + 12 = 60. Add 60 to the number set. Current number set: [60, 44], target: 22, just two numbers left.\n     |- Try 60 + 44 = 104. Evaluate 104 != 22, drop this branch.\n     |- Try 60 - 44 = 16. Evaluate 16 != 22, drop this branch.\n     |- Try 60 * 44 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 - 12 = 36. Add 36 to the number set. Current number set: [36, 44], target: 22, just two numbers left.\n     |- Try 44 + 36 = 80. Evaluate 80 != 22, drop this branch.\n     |- Try 44 - 36 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 44 * 36 = 1584. Evaluate 1584 != 22, drop this branch.\n     |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 12 = 576. Add 576 to the number set. Current number set: [576, 44], target: 22, just two numbers left.\n     |- Try 576 + 44 = 620. Evaluate 620 != 22, drop this branch.\n     |- Try 576 - 44 = 532. Evaluate 532 != 22, drop this branch.\n     |- Try 576 * 44 = 25344. 25344 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 44 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 48 \/ 12 = 4. Add 4 to the number set. Current number set: [4, 44], target: 22, just two numbers left.\n     |- Try 44 + 4 = 48. Evaluate 48 != 22, drop this branch.\n     |- Try 44 - 4 = 40. Evaluate 40 != 22, drop this branch.\n     |- Try 44 * 4 = 176. Evaluate 176 != 22, drop this branch.\n     |- Try 44 \/ 4 = 11. Evaluate 11 != 22, drop this branch.\n   |- Pick two numbers (48, 44) (numbers left: [12]). Try possible operations.\n    |- Try 48 + 44 = 92. Add 92 to the number set. Current number set: [92, 12], target: 22, just two numbers left.\n     |- Try 92 + 12 = 104. Evaluate 104 != 22, drop this branch.\n     |- Try 92 - 12 = 80. Evaluate 80 != 22, drop this branch.\n     |- Try 92 * 12 = 1104. Evaluate 1104 != 22, drop this branch.\n     |- Try 92 \/ 12 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 48 - 44 = 4. Add 4 to the number set. Current number set: [4, 12], target: 22, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 22, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 22, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 22, drop this branch.\n    |- Try 48 * 44 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (12, 44) (numbers left: [48]). Try possible operations.\n    |- Try 44 + 12 = 56. Add 56 to the number set. Current number set: [56, 48], target: 22, just two numbers left.\n     |- Try 56 + 48 = 104. Evaluate 104 != 22, drop this branch.\n     |- Try 56 - 48 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 56 * 48 = 2688. 2688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 - 12 = 32. Add 32 to the number set. Current number set: [32, 48], target: 22, just two numbers left.\n     |- Try 48 + 32 = 80. Evaluate 80 != 22, drop this branch.\n     |- Try 48 - 32 = 16. Evaluate 16 != 22, drop this branch.\n     |- Try 48 * 32 = 1536. Evaluate 1536 != 22, drop this branch.\n     |- Try 48 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 12 = 528. Add 528 to the number set. Current number set: [528, 48], target: 22, just two numbers left.\n     |- Try 528 + 48 = 576. Evaluate 576 != 22, drop this branch.\n     |- Try 528 - 48 = 480. Evaluate 480 != 22, drop this branch.\n     |- Try 528 * 48 = 25344. 25344 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 48 = 11. Evaluate 11 != 22, drop this branch.\n    |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 29 - 19 = 10. Add 10 to the number set. Current number set: [10, 12, 44], target: 22. Options for choosing two numbers: [(10, 12), (10, 44), (12, 44)].\n   |- Pick two numbers (10, 12) (numbers left: [44]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 44], target: 22, just two numbers left.\n     |- Try 44 + 22 = 66. Evaluate 66 != 22, drop this branch.\n     |- Try 44 - 22 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 22 = 22\nThe step before: 12 + 10 = 22\nThe first step: 29 - 19 = 10\n\nOutput the solution in the required format:\n<Solution>\n29 - 19 = 10\n12 + 10 = 22\n44 - 22 = 22\n<\/Solution>\n","item":{"nums":[19,29,12,44],"solution":["29 - 19 = 10","12 + 10 = 22","44 - 22 = 22"],"target":22}}
+{"instance_id":"countdown_2k_63","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 49, 29, 25]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [19, 49, 29, 25], target: 17. Options for choosing two numbers: [(19, 49), (19, 29), (19, 25), (49, 29), (49, 25), (29, 25)].\n |- Pick two numbers (19, 49) (numbers left: [29, 25]). Try possible operations.\n  |- Try 49 + 19 = 68. Add 68 to the number set. Current number set: [68, 29, 25], target: 17. Options for choosing two numbers: [(68, 29), (68, 25), (29, 25)].\n   |- Pick two numbers (68, 29) (numbers left: [25]). Try possible operations.\n    |- Try 68 + 29 = 97. Add 97 to the number set. Current number set: [97, 25], target: 17, just two numbers left.\n     |- Try 97 + 25 = 122. Evaluate 122 != 17, drop this branch.\n     |- Try 97 - 25 = 72. Evaluate 72 != 17, drop this branch.\n     |- Try 97 * 25 = 2425. 2425 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 25 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 68 - 29 = 39. Add 39 to the number set. Current number set: [39, 25], target: 17, just two numbers left.\n     |- Try 39 + 25 = 64. Evaluate 64 != 17, drop this branch.\n     |- Try 39 - 25 = 14. Evaluate 14 != 17, drop this branch.\n     |- Try 39 * 25 = 975. Evaluate 975 != 17, drop this branch.\n     |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 68 * 29 = 1972. Add 1972 to the number set. Current number set: [1972, 25], target: 17, just two numbers left.\n     |- Try 1972 + 25 = 1997. Evaluate 1997 != 17, drop this branch.\n     |- Try 1972 - 25 = 1947. Evaluate 1947 != 17, drop this branch.\n     |- Try 1972 * 25 = 49300. 49300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1972 \/ 25 = 78.9. 78.9 is a decimal, drop this branch.\n    |- Try 68 \/ 29 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (68, 25) (numbers left: [29]). Try possible operations.\n    |- Try 68 + 25 = 93. Add 93 to the number set. Current number set: [93, 29], target: 17, just two numbers left.\n     |- Try 93 + 29 = 122. Evaluate 122 != 17, drop this branch.\n     |- Try 93 - 29 = 64. Evaluate 64 != 17, drop this branch.\n     |- Try 93 * 29 = 2697. 2697 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 29 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 68 - 25 = 43. Add 43 to the number set. Current number set: [43, 29], target: 17, just two numbers left.\n     |- Try 43 + 29 = 72. Evaluate 72 != 17, drop this branch.\n     |- Try 43 - 29 = 14. Evaluate 14 != 17, drop this branch.\n     |- Try 43 * 29 = 1247. Evaluate 1247 != 17, drop this branch.\n     |- Try 43 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 68 * 25 = 1700. Add 1700 to the number set. Current number set: [1700, 29], target: 17, just two numbers left.\n     |- Try 1700 + 29 = 1729. Evaluate 1729 != 17, drop this branch.\n     |- Try 1700 - 29 = 1671. Evaluate 1671 != 17, drop this branch.\n     |- Try 1700 * 29 = 49300. 49300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1700 \/ 29 = 58.6. 58.6 is a decimal, drop this branch.\n    |- Try 68 \/ 25 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (29, 25) (numbers left: [68]). Try possible operations.\n    |- Try 29 + 25 = 54. Add 54 to the number set. Current number set: [54, 68], target: 17, just two numbers left.\n     |- Try 68 + 54 = 122. Evaluate 122 != 17, drop this branch.\n     |- Try 68 - 54 = 14. Evaluate 14 != 17, drop this branch.\n     |- Try 68 * 54 = 3672. 3672 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 54 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 29 - 25 = 4. Add 4 to the number set. Current number set: [4, 68], target: 17, just two numbers left.\n     |- Try 68 + 4 = 72. Evaluate 72 != 17, drop this branch.\n     |- Try 68 - 4 = 64. Evaluate 64 != 17, drop this branch.\n     |- Try 68 * 4 = 272. Evaluate 272 != 17, drop this branch.\n     |- Try 68 \/ 4 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 68 \/ 4 = 17\nThe step before: 29 - 25 = 4\nThe first step: 49 + 19 = 68\n\nOutput the solution in the required format:\n<Solution>\n49 + 19 = 68\n29 - 25 = 4\n68 \/ 4 = 17\n<\/Solution>\n","item":{"nums":[19,49,29,25],"solution":["49 + 19 = 68","29 - 25 = 4","68 \/ 4 = 17"],"target":17}}
+{"instance_id":"countdown_2k_64","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 8, 12, 43]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [13, 8, 12, 43], target: 26. Options for choosing two numbers: [(13, 8), (13, 12), (13, 43), (8, 12), (8, 43), (12, 43)].\n |- Pick two numbers (13, 8) (numbers left: [12, 43]). Try possible operations.\n  |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 12, 43], target: 26. Options for choosing two numbers: [(21, 12), (21, 43), (12, 43)].\n   |- Pick two numbers (21, 12) (numbers left: [43]). Try possible operations.\n    |- Try 21 + 12 = 33. Add 33 to the number set. Current number set: [33, 43], target: 26, just two numbers left.\n     |- Try 43 + 33 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 43 - 33 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 43 * 33 = 1419. Evaluate 1419 != 26, drop this branch.\n     |- Try 43 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 21 - 12 = 9. Add 9 to the number set. Current number set: [9, 43], target: 26, just two numbers left.\n     |- Try 43 + 9 = 52. Evaluate 52 != 26, drop this branch.\n     |- Try 43 - 9 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 43 * 9 = 387. Evaluate 387 != 26, drop this branch.\n     |- Try 43 \/ 9 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 21 * 12 = 252. Add 252 to the number set. Current number set: [252, 43], target: 26, just two numbers left.\n     |- Try 252 + 43 = 295. Evaluate 295 != 26, drop this branch.\n     |- Try 252 - 43 = 209. Evaluate 209 != 26, drop this branch.\n     |- Try 252 * 43 = 10836. 10836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 43 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 21 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (21, 43) (numbers left: [12]). Try possible operations.\n    |- Try 43 + 21 = 64. Add 64 to the number set. Current number set: [64, 12], target: 26, just two numbers left.\n     |- Try 64 + 12 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 64 - 12 = 52. Evaluate 52 != 26, drop this branch.\n     |- Try 64 * 12 = 768. Evaluate 768 != 26, drop this branch.\n     |- Try 64 \/ 12 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 43 - 21 = 22. Add 22 to the number set. Current number set: [22, 12], target: 26, just two numbers left.\n     |- Try 22 + 12 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 22 - 12 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 22 * 12 = 264. Evaluate 264 != 26, drop this branch.\n     |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 43 * 21 = 903. Add 903 to the number set. Current number set: [903, 12], target: 26, just two numbers left.\n     |- Try 903 + 12 = 915. Evaluate 915 != 26, drop this branch.\n     |- Try 903 - 12 = 891. Evaluate 891 != 26, drop this branch.\n     |- Try 903 * 12 = 10836. 10836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 903 \/ 12 = 75.2. 75.2 is a decimal, drop this branch.\n    |- Try 43 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (12, 43) (numbers left: [21]). Try possible operations.\n    |- Try 43 + 12 = 55. Add 55 to the number set. Current number set: [55, 21], target: 26, just two numbers left.\n     |- Try 55 + 21 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 55 - 21 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 55 * 21 = 1155. Evaluate 1155 != 26, drop this branch.\n     |- Try 55 \/ 21 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 43 - 12 = 31. Add 31 to the number set. Current number set: [31, 21], target: 26, just two numbers left.\n     |- Try 31 + 21 = 52. Evaluate 52 != 26, drop this branch.\n     |- Try 31 - 21 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 31 * 21 = 651. Evaluate 651 != 26, drop this branch.\n     |- Try 31 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 43 * 12 = 516. Add 516 to the number set. Current number set: [516, 21], target: 26, just two numbers left.\n     |- Try 516 + 21 = 537. Evaluate 537 != 26, drop this branch.\n     |- Try 516 - 21 = 495. Evaluate 495 != 26, drop this branch.\n     |- Try 516 * 21 = 10836. 10836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 516 \/ 21 = 24.6. 24.6 is a decimal, drop this branch.\n    |- Try 43 \/ 12 = 3.6. 3.6 is a decimal, drop this branch.\n  |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 12, 43], target: 26. Options for choosing two numbers: [(5, 12), (5, 43), (12, 43)].\n   |- Pick two numbers (5, 12) (numbers left: [43]). Try possible operations.\n    |- Try 12 + 5 = 17. Add 17 to the number set. Current number set: [17, 43], target: 26, just two numbers left.\n     |- Try 43 + 17 = 60. Evaluate 60 != 26, drop this branch.\n     |- Try 43 - 17 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 - 17 = 26\nThe step before: 12 + 5 = 17\nThe first step: 13 - 8 = 5\n\nOutput the solution in the required format:\n<Solution>\n13 - 8 = 5\n12 + 5 = 17\n43 - 17 = 26\n<\/Solution>\n","item":{"nums":[13,8,12,43],"solution":["13 - 8 = 5","12 + 5 = 17","43 - 17 = 26"],"target":26}}
+{"instance_id":"countdown_2k_65","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 46, 48, 42]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [15, 46, 48, 42], target: 25. Options for choosing two numbers: [(15, 46), (15, 48), (15, 42), (46, 48), (46, 42), (48, 42)].\n |- Pick two numbers (15, 46) (numbers left: [48, 42]). Try possible operations.\n  |- Try 46 + 15 = 61. Add 61 to the number set. Current number set: [61, 48, 42], target: 25. Options for choosing two numbers: [(61, 48), (61, 42), (48, 42)].\n   |- Pick two numbers (61, 48) (numbers left: [42]). Try possible operations.\n    |- Try 61 + 48 = 109. Add 109 to the number set. Current number set: [109, 42], target: 25, just two numbers left.\n     |- Try 109 + 42 = 151. Evaluate 151 != 25, drop this branch.\n     |- Try 109 - 42 = 67. Evaluate 67 != 25, drop this branch.\n     |- Try 109 * 42 = 4578. 4578 exceeds the maximum intermediate result, drop this branch.\n     |- Try 109 \/ 42 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 61 - 48 = 13. Add 13 to the number set. Current number set: [13, 42], target: 25, just two numbers left.\n     |- Try 42 + 13 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 42 - 13 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 42 * 13 = 546. Evaluate 546 != 25, drop this branch.\n     |- Try 42 \/ 13 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 61 * 48 = 2928. 2928 exceeds the maximum intermediate result, drop this branch.\n    |- Try 61 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (61, 42) (numbers left: [48]). Try possible operations.\n    |- Try 61 + 42 = 103. Add 103 to the number set. Current number set: [103, 48], target: 25, just two numbers left.\n     |- Try 103 + 48 = 151. Evaluate 151 != 25, drop this branch.\n     |- Try 103 - 48 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 103 * 48 = 4944. 4944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 48 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 61 - 42 = 19. Add 19 to the number set. Current number set: [19, 48], target: 25, just two numbers left.\n     |- Try 48 + 19 = 67. Evaluate 67 != 25, drop this branch.\n     |- Try 48 - 19 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 48 * 19 = 912. Evaluate 912 != 25, drop this branch.\n     |- Try 48 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 61 * 42 = 2562. 2562 exceeds the maximum intermediate result, drop this branch.\n    |- Try 61 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (48, 42) (numbers left: [61]). Try possible operations.\n    |- Try 48 + 42 = 90. Add 90 to the number set. Current number set: [90, 61], target: 25, just two numbers left.\n     |- Try 90 + 61 = 151. Evaluate 151 != 25, drop this branch.\n     |- Try 90 - 61 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 90 * 61 = 5490. 5490 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 61 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 42 = 6. Add 6 to the number set. Current number set: [6, 61], target: 25, just two numbers left.\n     |- Try 61 + 6 = 67. Evaluate 67 != 25, drop this branch.\n     |- Try 61 - 6 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 61 * 6 = 366. Evaluate 366 != 25, drop this branch.\n     |- Try 61 \/ 6 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 46 - 15 = 31. Add 31 to the number set. Current number set: [31, 48, 42], target: 25. Options for choosing two numbers: [(31, 48), (31, 42), (48, 42)].\n   |- Pick two numbers (31, 48) (numbers left: [42]). Try possible operations.\n    |- Try 48 + 31 = 79. Add 79 to the number set. Current number set: [79, 42], target: 25, just two numbers left.\n     |- Try 79 + 42 = 121. Evaluate 121 != 25, drop this branch.\n     |- Try 79 - 42 = 37. Evaluate 37 != 25, drop this branch.\n     |- Try 79 * 42 = 3318. 3318 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 42 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 48 - 31 = 17. Add 17 to the number set. Current number set: [17, 42], target: 25, just two numbers left.\n     |- Try 42 + 17 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 42 - 17 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 42 - 17 = 25\nThe step before: 48 - 31 = 17\nThe first step: 46 - 15 = 31\n\nOutput the solution in the required format:\n<Solution>\n46 - 15 = 31\n48 - 31 = 17\n42 - 17 = 25\n<\/Solution>\n","item":{"nums":[15,46,48,42],"solution":["46 - 15 = 31","48 - 31 = 17","42 - 17 = 25"],"target":25}}
+{"instance_id":"countdown_2k_66","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 2, 16, 3]\nTarget: 19","reference_output":"# Search Procedure\nInitial number set: [27, 2, 16, 3], target: 19. Options for choosing two numbers: [(27, 2), (27, 16), (27, 3), (2, 16), (2, 3), (16, 3)].\n |- Pick two numbers (27, 2) (numbers left: [16, 3]). Try possible operations.\n  |- Try 27 + 2 = 29. Add 29 to the number set. Current number set: [29, 16, 3], target: 19. Options for choosing two numbers: [(29, 16), (29, 3), (16, 3)].\n   |- Pick two numbers (29, 16) (numbers left: [3]). Try possible operations.\n    |- Try 29 + 16 = 45. Add 45 to the number set. Current number set: [45, 3], target: 19, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 19, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 19, drop this branch.\n    |- Try 29 - 16 = 13. Add 13 to the number set. Current number set: [13, 3], target: 19, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 19, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 19, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 != 19, drop this branch.\n     |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 29 * 16 = 464. Add 464 to the number set. Current number set: [464, 3], target: 19, just two numbers left.\n     |- Try 464 + 3 = 467. Evaluate 467 != 19, drop this branch.\n     |- Try 464 - 3 = 461. Evaluate 461 != 19, drop this branch.\n     |- Try 464 * 3 = 1392. Evaluate 1392 != 19, drop this branch.\n     |- Try 464 \/ 3 = 154.7. 154.7 is a decimal, drop this branch.\n    |- Try 29 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (29, 3) (numbers left: [16]). Try possible operations.\n    |- Try 29 + 3 = 32. Add 32 to the number set. Current number set: [32, 16], target: 19, just two numbers left.\n     |- Try 32 + 16 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 32 - 16 = 16. Evaluate 16 != 19, drop this branch.\n     |- Try 32 * 16 = 512. Evaluate 512 != 19, drop this branch.\n     |- Try 32 \/ 16 = 2. Evaluate 2 != 19, drop this branch.\n    |- Try 29 - 3 = 26. Add 26 to the number set. Current number set: [26, 16], target: 19, just two numbers left.\n     |- Try 26 + 16 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 26 - 16 = 10. Evaluate 10 != 19, drop this branch.\n     |- Try 26 * 16 = 416. Evaluate 416 != 19, drop this branch.\n     |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 29 * 3 = 87. Add 87 to the number set. Current number set: [87, 16], target: 19, just two numbers left.\n     |- Try 87 + 16 = 103. Evaluate 103 != 19, drop this branch.\n     |- Try 87 - 16 = 71. Evaluate 71 != 19, drop this branch.\n     |- Try 87 * 16 = 1392. Evaluate 1392 != 19, drop this branch.\n     |- Try 87 \/ 16 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n   |- Pick two numbers (16, 3) (numbers left: [29]). Try possible operations.\n    |- Try 16 + 3 = 19. Add 19 to the number set. Current number set: [19, 29], target: 19, just two numbers left.\n     |- Try 29 + 19 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 29 - 19 = 10. Evaluate 10 != 19, drop this branch.\n     |- Try 29 * 19 = 551. Evaluate 551 != 19, drop this branch.\n     |- Try 29 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 16 - 3 = 13. Add 13 to the number set. Current number set: [13, 29], target: 19, just two numbers left.\n     |- Try 29 + 13 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 29 - 13 = 16. Evaluate 16 != 19, drop this branch.\n     |- Try 29 * 13 = 377. Evaluate 377 != 19, drop this branch.\n     |- Try 29 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 * 3 = 48. Add 48 to the number set. Current number set: [48, 29], target: 19, just two numbers left.\n     |- Try 48 + 29 = 77. Evaluate 77 != 19, drop this branch.\n     |- Try 48 - 29 = 19. Evaluate 19 == 19, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 29 = 19\nThe step before: 16 * 3 = 48\nThe first step: 27 + 2 = 29\n\nOutput the solution in the required format:\n<Solution>\n27 + 2 = 29\n16 * 3 = 48\n48 - 29 = 19\n<\/Solution>\n","item":{"nums":[27,2,16,3],"solution":["27 + 2 = 29","16 * 3 = 48","48 - 29 = 19"],"target":19}}
+{"instance_id":"countdown_2k_67","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 34, 8, 34]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [37, 34, 8, 34], target: 10. Options for choosing two numbers: [(37, 34), (37, 8), (37, 34), (34, 8), (34, 34), (8, 34)].\n |- Pick two numbers (37, 34) (numbers left: [8, 34]). Try possible operations.\n  |- Try 37 + 34 = 71. Add 71 to the number set. Current number set: [71, 8, 34], target: 10. Options for choosing two numbers: [(71, 8), (71, 34), (8, 34)].\n   |- Pick two numbers (71, 8) (numbers left: [34]). Try possible operations.\n    |- Try 71 + 8 = 79. Add 79 to the number set. Current number set: [79, 34], target: 10, just two numbers left.\n     |- Try 79 + 34 = 113. Evaluate 113 != 10, drop this branch.\n     |- Try 79 - 34 = 45. Evaluate 45 != 10, drop this branch.\n     |- Try 79 * 34 = 2686. 2686 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 34 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 71 - 8 = 63. Add 63 to the number set. Current number set: [63, 34], target: 10, just two numbers left.\n     |- Try 63 + 34 = 97. Evaluate 97 != 10, drop this branch.\n     |- Try 63 - 34 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 63 * 34 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 34 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 71 * 8 = 568. Add 568 to the number set. Current number set: [568, 34], target: 10, just two numbers left.\n     |- Try 568 + 34 = 602. Evaluate 602 != 10, drop this branch.\n     |- Try 568 - 34 = 534. Evaluate 534 != 10, drop this branch.\n     |- Try 568 * 34 = 19312. 19312 exceeds the maximum intermediate result, drop this branch.\n     |- Try 568 \/ 34 = 16.7. 16.7 is a decimal, drop this branch.\n    |- Try 71 \/ 8 = 8.9. 8.9 is a decimal, drop this branch.\n   |- Pick two numbers (71, 34) (numbers left: [8]). Try possible operations.\n    |- Try 71 + 34 = 105. Add 105 to the number set. Current number set: [105, 8], target: 10, just two numbers left.\n     |- Try 105 + 8 = 113. Evaluate 113 != 10, drop this branch.\n     |- Try 105 - 8 = 97. Evaluate 97 != 10, drop this branch.\n     |- Try 105 * 8 = 840. Evaluate 840 != 10, drop this branch.\n     |- Try 105 \/ 8 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 71 - 34 = 37. Add 37 to the number set. Current number set: [37, 8], target: 10, just two numbers left.\n     |- Try 37 + 8 = 45. Evaluate 45 != 10, drop this branch.\n     |- Try 37 - 8 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 37 * 8 = 296. Evaluate 296 != 10, drop this branch.\n     |- Try 37 \/ 8 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 71 * 34 = 2414. 2414 exceeds the maximum intermediate result, drop this branch.\n    |- Try 71 \/ 34 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (8, 34) (numbers left: [71]). Try possible operations.\n    |- Try 34 + 8 = 42. Add 42 to the number set. Current number set: [42, 71], target: 10, just two numbers left.\n     |- Try 71 + 42 = 113. Evaluate 113 != 10, drop this branch.\n     |- Try 71 - 42 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 71 * 42 = 2982. 2982 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 42 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 34 - 8 = 26. Add 26 to the number set. Current number set: [26, 71], target: 10, just two numbers left.\n     |- Try 71 + 26 = 97. Evaluate 97 != 10, drop this branch.\n     |- Try 71 - 26 = 45. Evaluate 45 != 10, drop this branch.\n     |- Try 71 * 26 = 1846. Evaluate 1846 != 10, drop this branch.\n     |- Try 71 \/ 26 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 34 * 8 = 272. Add 272 to the number set. Current number set: [272, 71], target: 10, just two numbers left.\n     |- Try 272 + 71 = 343. Evaluate 343 != 10, drop this branch.\n     |- Try 272 - 71 = 201. Evaluate 201 != 10, drop this branch.\n     |- Try 272 * 71 = 19312. 19312 exceeds the maximum intermediate result, drop this branch.\n     |- Try 272 \/ 71 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 34 \/ 8 = 4.2. 4.2 is a decimal, drop this branch.\n  |- Try 37 - 34 = 3. Add 3 to the number set. Current number set: [3, 8, 34], target: 10. Options for choosing two numbers: [(3, 8), (3, 34), (8, 34)].\n   |- Pick two numbers (3, 8) (numbers left: [34]). Try possible operations.\n    |- Try 8 + 3 = 11. Add 11 to the number set. Current number set: [11, 34], target: 10, just two numbers left.\n     |- Try 34 + 11 = 45. Evaluate 45 != 10, drop this branch.\n     |- Try 34 - 11 = 23. Evaluate 23 != 10, drop this branch.\n     |- Try 34 * 11 = 374. Evaluate 374 != 10, drop this branch.\n     |- Try 34 \/ 11 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 8 - 3 = 5. Add 5 to the number set. Current number set: [5, 34], target: 10, just two numbers left.\n     |- Try 34 + 5 = 39. Evaluate 39 != 10, drop this branch.\n     |- Try 34 - 5 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 34 * 5 = 170. Evaluate 170 != 10, drop this branch.\n     |- Try 34 \/ 5 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 8 * 3 = 24. Add 24 to the number set. Current number set: [24, 34], target: 10, just two numbers left.\n     |- Try 34 + 24 = 58. Evaluate 58 != 10, drop this branch.\n     |- Try 34 - 24 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 - 24 = 10\nThe step before: 8 * 3 = 24\nThe first step: 37 - 34 = 3\n\nOutput the solution in the required format:\n<Solution>\n37 - 34 = 3\n8 * 3 = 24\n34 - 24 = 10\n<\/Solution>\n","item":{"nums":[37,34,8,34],"solution":["37 - 34 = 3","8 * 3 = 24","34 - 24 = 10"],"target":10}}
+{"instance_id":"countdown_2k_68","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 44, 26, 49]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [18, 44, 26, 49], target: 49. Options for choosing two numbers: [(18, 44), (18, 26), (18, 49), (44, 26), (44, 49), (26, 49)].\n |- Pick two numbers (18, 44) (numbers left: [26, 49]). Try possible operations.\n  |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 26, 49], target: 49. Options for choosing two numbers: [(62, 26), (62, 49), (26, 49)].\n   |- Pick two numbers (62, 26) (numbers left: [49]). Try possible operations.\n    |- Try 62 + 26 = 88. Add 88 to the number set. Current number set: [88, 49], target: 49, just two numbers left.\n     |- Try 88 + 49 = 137. Evaluate 137 != 49, drop this branch.\n     |- Try 88 - 49 = 39. Evaluate 39 != 49, drop this branch.\n     |- Try 88 * 49 = 4312. 4312 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 49 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 62 - 26 = 36. Add 36 to the number set. Current number set: [36, 49], target: 49, just two numbers left.\n     |- Try 49 + 36 = 85. Evaluate 85 != 49, drop this branch.\n     |- Try 49 - 36 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 49 * 36 = 1764. Evaluate 1764 != 49, drop this branch.\n     |- Try 49 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 62 * 26 = 1612. Add 1612 to the number set. Current number set: [1612, 49], target: 49, just two numbers left.\n     |- Try 1612 + 49 = 1661. Evaluate 1661 != 49, drop this branch.\n     |- Try 1612 - 49 = 1563. Evaluate 1563 != 49, drop this branch.\n     |- Try 1612 * 49 = 78988. 78988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1612 \/ 49 = 32.9. 32.9 is a decimal, drop this branch.\n    |- Try 62 \/ 26 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (62, 49) (numbers left: [26]). Try possible operations.\n    |- Try 62 + 49 = 111. Add 111 to the number set. Current number set: [111, 26], target: 49, just two numbers left.\n     |- Try 111 + 26 = 137. Evaluate 137 != 49, drop this branch.\n     |- Try 111 - 26 = 85. Evaluate 85 != 49, drop this branch.\n     |- Try 111 * 26 = 2886. 2886 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 26 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 62 - 49 = 13. Add 13 to the number set. Current number set: [13, 26], target: 49, just two numbers left.\n     |- Try 26 + 13 = 39. Evaluate 39 != 49, drop this branch.\n     |- Try 26 - 13 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 26 * 13 = 338. Evaluate 338 != 49, drop this branch.\n     |- Try 26 \/ 13 = 2. Evaluate 2 != 49, drop this branch.\n    |- Try 62 * 49 = 3038. 3038 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 49 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (26, 49) (numbers left: [62]). Try possible operations.\n    |- Try 49 + 26 = 75. Add 75 to the number set. Current number set: [75, 62], target: 49, just two numbers left.\n     |- Try 75 + 62 = 137. Evaluate 137 != 49, drop this branch.\n     |- Try 75 - 62 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 75 * 62 = 4650. 4650 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 62 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 - 26 = 23. Add 23 to the number set. Current number set: [23, 62], target: 49, just two numbers left.\n     |- Try 62 + 23 = 85. Evaluate 85 != 49, drop this branch.\n     |- Try 62 - 23 = 39. Evaluate 39 != 49, drop this branch.\n     |- Try 62 * 23 = 1426. Evaluate 1426 != 49, drop this branch.\n     |- Try 62 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 49 * 26 = 1274. Add 1274 to the number set. Current number set: [1274, 62], target: 49, just two numbers left.\n     |- Try 1274 + 62 = 1336. Evaluate 1336 != 49, drop this branch.\n     |- Try 1274 - 62 = 1212. Evaluate 1212 != 49, drop this branch.\n     |- Try 1274 * 62 = 78988. 78988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1274 \/ 62 = 20.5. 20.5 is a decimal, drop this branch.\n    |- Try 49 \/ 26 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 26, 49], target: 49. Options for choosing two numbers: [(26, 26), (26, 49), (26, 49)].\n   |- Pick two numbers (26, 26) (numbers left: [49]). Try possible operations.\n    |- Try 26 + 26 = 52. Add 52 to the number set. Current number set: [52, 49], target: 49, just two numbers left.\n     |- Try 52 + 49 = 101. Evaluate 101 != 49, drop this branch.\n     |- Try 52 - 49 = 3. Evaluate 3 != 49, drop this branch.\n     |- Try 52 * 49 = 2548. 2548 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 - 26 = 0. Add 0 to the number set. Current number set: [0, 49], target: 49, just two numbers left.\n     |- Try 49 + 0 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 + 0 = 49\nThe step before: 26 - 26 = 0\nThe first step: 44 - 18 = 26\n\nOutput the solution in the required format:\n<Solution>\n44 - 18 = 26\n26 - 26 = 0\n49 + 0 = 49\n<\/Solution>\n","item":{"nums":[18,44,26,49],"solution":["44 - 18 = 26","26 - 26 = 0","49 + 0 = 49"],"target":49}}
+{"instance_id":"countdown_2k_69","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 38, 13, 34]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [26, 38, 13, 34], target: 35. Options for choosing two numbers: [(26, 38), (26, 13), (26, 34), (38, 13), (38, 34), (13, 34)].\n |- Pick two numbers (26, 38) (numbers left: [13, 34]). Try possible operations.\n  |- Try 38 + 26 = 64. Add 64 to the number set. Current number set: [64, 13, 34], target: 35. Options for choosing two numbers: [(64, 13), (64, 34), (13, 34)].\n   |- Pick two numbers (64, 13) (numbers left: [34]). Try possible operations.\n    |- Try 64 + 13 = 77. Add 77 to the number set. Current number set: [77, 34], target: 35, just two numbers left.\n     |- Try 77 + 34 = 111. Evaluate 111 != 35, drop this branch.\n     |- Try 77 - 34 = 43. Evaluate 43 != 35, drop this branch.\n     |- Try 77 * 34 = 2618. 2618 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 34 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 64 - 13 = 51. Add 51 to the number set. Current number set: [51, 34], target: 35, just two numbers left.\n     |- Try 51 + 34 = 85. Evaluate 85 != 35, drop this branch.\n     |- Try 51 - 34 = 17. Evaluate 17 != 35, drop this branch.\n     |- Try 51 * 34 = 1734. Evaluate 1734 != 35, drop this branch.\n     |- Try 51 \/ 34 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 64 * 13 = 832. Add 832 to the number set. Current number set: [832, 34], target: 35, just two numbers left.\n     |- Try 832 + 34 = 866. Evaluate 866 != 35, drop this branch.\n     |- Try 832 - 34 = 798. Evaluate 798 != 35, drop this branch.\n     |- Try 832 * 34 = 28288. 28288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 832 \/ 34 = 24.5. 24.5 is a decimal, drop this branch.\n    |- Try 64 \/ 13 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (64, 34) (numbers left: [13]). Try possible operations.\n    |- Try 64 + 34 = 98. Add 98 to the number set. Current number set: [98, 13], target: 35, just two numbers left.\n     |- Try 98 + 13 = 111. Evaluate 111 != 35, drop this branch.\n     |- Try 98 - 13 = 85. Evaluate 85 != 35, drop this branch.\n     |- Try 98 * 13 = 1274. Evaluate 1274 != 35, drop this branch.\n     |- Try 98 \/ 13 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 64 - 34 = 30. Add 30 to the number set. Current number set: [30, 13], target: 35, just two numbers left.\n     |- Try 30 + 13 = 43. Evaluate 43 != 35, drop this branch.\n     |- Try 30 - 13 = 17. Evaluate 17 != 35, drop this branch.\n     |- Try 30 * 13 = 390. Evaluate 390 != 35, drop this branch.\n     |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 64 * 34 = 2176. 2176 exceeds the maximum intermediate result, drop this branch.\n    |- Try 64 \/ 34 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (13, 34) (numbers left: [64]). Try possible operations.\n    |- Try 34 + 13 = 47. Add 47 to the number set. Current number set: [47, 64], target: 35, just two numbers left.\n     |- Try 64 + 47 = 111. Evaluate 111 != 35, drop this branch.\n     |- Try 64 - 47 = 17. Evaluate 17 != 35, drop this branch.\n     |- Try 64 * 47 = 3008. 3008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 47 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 34 - 13 = 21. Add 21 to the number set. Current number set: [21, 64], target: 35, just two numbers left.\n     |- Try 64 + 21 = 85. Evaluate 85 != 35, drop this branch.\n     |- Try 64 - 21 = 43. Evaluate 43 != 35, drop this branch.\n     |- Try 64 * 21 = 1344. Evaluate 1344 != 35, drop this branch.\n     |- Try 64 \/ 21 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 34 * 13 = 442. Add 442 to the number set. Current number set: [442, 64], target: 35, just two numbers left.\n     |- Try 442 + 64 = 506. Evaluate 506 != 35, drop this branch.\n     |- Try 442 - 64 = 378. Evaluate 378 != 35, drop this branch.\n     |- Try 442 * 64 = 28288. 28288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 442 \/ 64 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 34 \/ 13 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 38 - 26 = 12. Add 12 to the number set. Current number set: [12, 13, 34], target: 35. Options for choosing two numbers: [(12, 13), (12, 34), (13, 34)].\n   |- Pick two numbers (12, 13) (numbers left: [34]). Try possible operations.\n    |- Try 13 + 12 = 25. Add 25 to the number set. Current number set: [25, 34], target: 35, just two numbers left.\n     |- Try 34 + 25 = 59. Evaluate 59 != 35, drop this branch.\n     |- Try 34 - 25 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 34 * 25 = 850. Evaluate 850 != 35, drop this branch.\n     |- Try 34 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 13 - 12 = 1. Add 1 to the number set. Current number set: [1, 34], target: 35, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 1 = 35\nThe step before: 13 - 12 = 1\nThe first step: 38 - 26 = 12\n\nOutput the solution in the required format:\n<Solution>\n38 - 26 = 12\n13 - 12 = 1\n34 + 1 = 35\n<\/Solution>\n","item":{"nums":[26,38,13,34],"solution":["38 - 26 = 12","13 - 12 = 1","34 + 1 = 35"],"target":35}}
+{"instance_id":"countdown_2k_70","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [38, 23, 23, 18]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [38, 23, 23, 18], target: 10. Options for choosing two numbers: [(38, 23), (38, 23), (38, 18), (23, 23), (23, 18), (23, 18)].\n |- Pick two numbers (38, 23) (numbers left: [23, 18]). Try possible operations.\n  |- Try 38 + 23 = 61. Add 61 to the number set. Current number set: [61, 23, 18], target: 10. Options for choosing two numbers: [(61, 23), (61, 18), (23, 18)].\n   |- Pick two numbers (61, 23) (numbers left: [18]). Try possible operations.\n    |- Try 61 + 23 = 84. Add 84 to the number set. Current number set: [84, 18], target: 10, just two numbers left.\n     |- Try 84 + 18 = 102. Evaluate 102 != 10, drop this branch.\n     |- Try 84 - 18 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 84 * 18 = 1512. Evaluate 1512 != 10, drop this branch.\n     |- Try 84 \/ 18 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 61 - 23 = 38. Add 38 to the number set. Current number set: [38, 18], target: 10, just two numbers left.\n     |- Try 38 + 18 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 38 - 18 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 38 * 18 = 684. Evaluate 684 != 10, drop this branch.\n     |- Try 38 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 61 * 23 = 1403. Add 1403 to the number set. Current number set: [1403, 18], target: 10, just two numbers left.\n     |- Try 1403 + 18 = 1421. Evaluate 1421 != 10, drop this branch.\n     |- Try 1403 - 18 = 1385. Evaluate 1385 != 10, drop this branch.\n     |- Try 1403 * 18 = 25254. 25254 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1403 \/ 18 = 77.9. 77.9 is a decimal, drop this branch.\n    |- Try 61 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (61, 18) (numbers left: [23]). Try possible operations.\n    |- Try 61 + 18 = 79. Add 79 to the number set. Current number set: [79, 23], target: 10, just two numbers left.\n     |- Try 79 + 23 = 102. Evaluate 102 != 10, drop this branch.\n     |- Try 79 - 23 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 79 * 23 = 1817. Evaluate 1817 != 10, drop this branch.\n     |- Try 79 \/ 23 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 61 - 18 = 43. Add 43 to the number set. Current number set: [43, 23], target: 10, just two numbers left.\n     |- Try 43 + 23 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 43 - 23 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 43 * 23 = 989. Evaluate 989 != 10, drop this branch.\n     |- Try 43 \/ 23 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 61 * 18 = 1098. Add 1098 to the number set. Current number set: [1098, 23], target: 10, just two numbers left.\n     |- Try 1098 + 23 = 1121. Evaluate 1121 != 10, drop this branch.\n     |- Try 1098 - 23 = 1075. Evaluate 1075 != 10, drop this branch.\n     |- Try 1098 * 23 = 25254. 25254 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1098 \/ 23 = 47.7. 47.7 is a decimal, drop this branch.\n    |- Try 61 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (23, 18) (numbers left: [61]). Try possible operations.\n    |- Try 23 + 18 = 41. Add 41 to the number set. Current number set: [41, 61], target: 10, just two numbers left.\n     |- Try 61 + 41 = 102. Evaluate 102 != 10, drop this branch.\n     |- Try 61 - 41 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 61 * 41 = 2501. 2501 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 23 - 18 = 5. Add 5 to the number set. Current number set: [5, 61], target: 10, just two numbers left.\n     |- Try 61 + 5 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 61 - 5 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 61 * 5 = 305. Evaluate 305 != 10, drop this branch.\n     |- Try 61 \/ 5 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 23 * 18 = 414. Add 414 to the number set. Current number set: [414, 61], target: 10, just two numbers left.\n     |- Try 414 + 61 = 475. Evaluate 475 != 10, drop this branch.\n     |- Try 414 - 61 = 353. Evaluate 353 != 10, drop this branch.\n     |- Try 414 * 61 = 25254. 25254 exceeds the maximum intermediate result, drop this branch.\n     |- Try 414 \/ 61 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 23 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 38 - 23 = 15. Add 15 to the number set. Current number set: [15, 23, 18], target: 10. Options for choosing two numbers: [(15, 23), (15, 18), (23, 18)].\n   |- Pick two numbers (15, 23) (numbers left: [18]). Try possible operations.\n    |- Try 23 + 15 = 38. Add 38 to the number set. Current number set: [38, 18], target: 10, just two numbers left.\n     |- Try 38 + 18 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 38 - 18 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 38 * 18 = 684. Evaluate 684 != 10, drop this branch.\n     |- Try 38 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 23 - 15 = 8. Add 8 to the number set. Current number set: [8, 18], target: 10, just two numbers left.\n     |- Try 18 + 8 = 26. Evaluate 26 != 10, drop this branch.\n     |- Try 18 - 8 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 18 - 8 = 10\nThe step before: 23 - 15 = 8\nThe first step: 38 - 23 = 15\n\nOutput the solution in the required format:\n<Solution>\n38 - 23 = 15\n23 - 15 = 8\n18 - 8 = 10\n<\/Solution>\n","item":{"nums":[38,23,23,18],"solution":["38 - 23 = 15","23 - 15 = 8","18 - 8 = 10"],"target":10}}
+{"instance_id":"countdown_2k_71","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 10, 7, 8]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [23, 10, 7, 8], target: 23. Options for choosing two numbers: [(23, 10), (23, 7), (23, 8), (10, 7), (10, 8), (7, 8)].\n |- Pick two numbers (23, 10) (numbers left: [7, 8]). Try possible operations.\n  |- Try 23 + 10 = 33. Add 33 to the number set. Current number set: [33, 7, 8], target: 23. Options for choosing two numbers: [(33, 7), (33, 8), (7, 8)].\n   |- Pick two numbers (33, 7) (numbers left: [8]). Try possible operations.\n    |- Try 33 + 7 = 40. Add 40 to the number set. Current number set: [40, 8], target: 23, just two numbers left.\n     |- Try 40 + 8 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 40 - 8 = 32. Evaluate 32 != 23, drop this branch.\n     |- Try 40 * 8 = 320. Evaluate 320 != 23, drop this branch.\n     |- Try 40 \/ 8 = 5. Evaluate 5 != 23, drop this branch.\n    |- Try 33 - 7 = 26. Add 26 to the number set. Current number set: [26, 8], target: 23, just two numbers left.\n     |- Try 26 + 8 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 26 - 8 = 18. Evaluate 18 != 23, drop this branch.\n     |- Try 26 * 8 = 208. Evaluate 208 != 23, drop this branch.\n     |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 33 * 7 = 231. Add 231 to the number set. Current number set: [231, 8], target: 23, just two numbers left.\n     |- Try 231 + 8 = 239. Evaluate 239 != 23, drop this branch.\n     |- Try 231 - 8 = 223. Evaluate 223 != 23, drop this branch.\n     |- Try 231 * 8 = 1848. Evaluate 1848 != 23, drop this branch.\n     |- Try 231 \/ 8 = 28.9. 28.9 is a decimal, drop this branch.\n    |- Try 33 \/ 7 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (33, 8) (numbers left: [7]). Try possible operations.\n    |- Try 33 + 8 = 41. Add 41 to the number set. Current number set: [41, 7], target: 23, just two numbers left.\n     |- Try 41 + 7 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 41 - 7 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 41 * 7 = 287. Evaluate 287 != 23, drop this branch.\n     |- Try 41 \/ 7 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 33 - 8 = 25. Add 25 to the number set. Current number set: [25, 7], target: 23, just two numbers left.\n     |- Try 25 + 7 = 32. Evaluate 32 != 23, drop this branch.\n     |- Try 25 - 7 = 18. Evaluate 18 != 23, drop this branch.\n     |- Try 25 * 7 = 175. Evaluate 175 != 23, drop this branch.\n     |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 33 * 8 = 264. Add 264 to the number set. Current number set: [264, 7], target: 23, just two numbers left.\n     |- Try 264 + 7 = 271. Evaluate 271 != 23, drop this branch.\n     |- Try 264 - 7 = 257. Evaluate 257 != 23, drop this branch.\n     |- Try 264 * 7 = 1848. Evaluate 1848 != 23, drop this branch.\n     |- Try 264 \/ 7 = 37.7. 37.7 is a decimal, drop this branch.\n    |- Try 33 \/ 8 = 4.1. 4.1 is a decimal, drop this branch.\n   |- Pick two numbers (7, 8) (numbers left: [33]). Try possible operations.\n    |- Try 8 + 7 = 15. Add 15 to the number set. Current number set: [15, 33], target: 23, just two numbers left.\n     |- Try 33 + 15 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 33 - 15 = 18. Evaluate 18 != 23, drop this branch.\n     |- Try 33 * 15 = 495. Evaluate 495 != 23, drop this branch.\n     |- Try 33 \/ 15 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 8 - 7 = 1. Add 1 to the number set. Current number set: [1, 33], target: 23, just two numbers left.\n     |- Try 33 + 1 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 33 - 1 = 32. Evaluate 32 != 23, drop this branch.\n     |- Try 33 * 1 = 33. Evaluate 33 != 23, drop this branch.\n     |- Try 33 \/ 1 = 33. Evaluate 33 != 23, drop this branch.\n    |- Try 8 * 7 = 56. Add 56 to the number set. Current number set: [56, 33], target: 23, just two numbers left.\n     |- Try 56 + 33 = 89. Evaluate 89 != 23, drop this branch.\n     |- Try 56 - 33 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 56 - 33 = 23\nThe step before: 8 * 7 = 56\nThe first step: 23 + 10 = 33\n\nOutput the solution in the required format:\n<Solution>\n23 + 10 = 33\n8 * 7 = 56\n56 - 33 = 23\n<\/Solution>\n","item":{"nums":[23,10,7,8],"solution":["23 + 10 = 33","8 * 7 = 56","56 - 33 = 23"],"target":23}}
+{"instance_id":"countdown_2k_72","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [2, 9, 47, 16]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [2, 9, 47, 16], target: 38. Options for choosing two numbers: [(2, 9), (2, 47), (2, 16), (9, 47), (9, 16), (47, 16)].\n |- Pick two numbers (2, 9) (numbers left: [47, 16]). Try possible operations.\n  |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 47, 16], target: 38. Options for choosing two numbers: [(11, 47), (11, 16), (47, 16)].\n   |- Pick two numbers (11, 47) (numbers left: [16]). Try possible operations.\n    |- Try 47 + 11 = 58. Add 58 to the number set. Current number set: [58, 16], target: 38, just two numbers left.\n     |- Try 58 + 16 = 74. Evaluate 74 != 38, drop this branch.\n     |- Try 58 - 16 = 42. Evaluate 42 != 38, drop this branch.\n     |- Try 58 * 16 = 928. Evaluate 928 != 38, drop this branch.\n     |- Try 58 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 47 - 11 = 36. Add 36 to the number set. Current number set: [36, 16], target: 38, just two numbers left.\n     |- Try 36 + 16 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 36 - 16 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 36 * 16 = 576. Evaluate 576 != 38, drop this branch.\n     |- Try 36 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 47 * 11 = 517. Add 517 to the number set. Current number set: [517, 16], target: 38, just two numbers left.\n     |- Try 517 + 16 = 533. Evaluate 533 != 38, drop this branch.\n     |- Try 517 - 16 = 501. Evaluate 501 != 38, drop this branch.\n     |- Try 517 * 16 = 8272. 8272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 517 \/ 16 = 32.3. 32.3 is a decimal, drop this branch.\n    |- Try 47 \/ 11 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (11, 16) (numbers left: [47]). Try possible operations.\n    |- Try 16 + 11 = 27. Add 27 to the number set. Current number set: [27, 47], target: 38, just two numbers left.\n     |- Try 47 + 27 = 74. Evaluate 74 != 38, drop this branch.\n     |- Try 47 - 27 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 47 * 27 = 1269. Evaluate 1269 != 38, drop this branch.\n     |- Try 47 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 16 - 11 = 5. Add 5 to the number set. Current number set: [5, 47], target: 38, just two numbers left.\n     |- Try 47 + 5 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 47 - 5 = 42. Evaluate 42 != 38, drop this branch.\n     |- Try 47 * 5 = 235. Evaluate 235 != 38, drop this branch.\n     |- Try 47 \/ 5 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 16 * 11 = 176. Add 176 to the number set. Current number set: [176, 47], target: 38, just two numbers left.\n     |- Try 176 + 47 = 223. Evaluate 223 != 38, drop this branch.\n     |- Try 176 - 47 = 129. Evaluate 129 != 38, drop this branch.\n     |- Try 176 * 47 = 8272. 8272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 47 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (47, 16) (numbers left: [11]). Try possible operations.\n    |- Try 47 + 16 = 63. Add 63 to the number set. Current number set: [63, 11], target: 38, just two numbers left.\n     |- Try 63 + 11 = 74. Evaluate 74 != 38, drop this branch.\n     |- Try 63 - 11 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 63 * 11 = 693. Evaluate 693 != 38, drop this branch.\n     |- Try 63 \/ 11 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 47 - 16 = 31. Add 31 to the number set. Current number set: [31, 11], target: 38, just two numbers left.\n     |- Try 31 + 11 = 42. Evaluate 42 != 38, drop this branch.\n     |- Try 31 - 11 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 31 * 11 = 341. Evaluate 341 != 38, drop this branch.\n     |- Try 31 \/ 11 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 47 * 16 = 752. Add 752 to the number set. Current number set: [752, 11], target: 38, just two numbers left.\n     |- Try 752 + 11 = 763. Evaluate 763 != 38, drop this branch.\n     |- Try 752 - 11 = 741. Evaluate 741 != 38, drop this branch.\n     |- Try 752 * 11 = 8272. 8272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 752 \/ 11 = 68.4. 68.4 is a decimal, drop this branch.\n    |- Try 47 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 47, 16], target: 38. Options for choosing two numbers: [(7, 47), (7, 16), (47, 16)].\n   |- Pick two numbers (7, 47) (numbers left: [16]). Try possible operations.\n    |- Try 47 + 7 = 54. Add 54 to the number set. Current number set: [54, 16], target: 38, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 38, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 54 - 16 = 38\nThe step before: 47 + 7 = 54\nThe first step: 9 - 2 = 7\n\nOutput the solution in the required format:\n<Solution>\n9 - 2 = 7\n47 + 7 = 54\n54 - 16 = 38\n<\/Solution>\n","item":{"nums":[2,9,47,16],"solution":["9 - 2 = 7","47 + 7 = 54","54 - 16 = 38"],"target":38}}
+{"instance_id":"countdown_2k_73","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 5, 12, 9]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [13, 5, 12, 9], target: 36. Options for choosing two numbers: [(13, 5), (13, 12), (13, 9), (5, 12), (5, 9), (12, 9)].\n |- Pick two numbers (13, 5) (numbers left: [12, 9]). Try possible operations.\n  |- Try 13 + 5 = 18. Add 18 to the number set. Current number set: [18, 12, 9], target: 36. Options for choosing two numbers: [(18, 12), (18, 9), (12, 9)].\n   |- Pick two numbers (18, 12) (numbers left: [9]). Try possible operations.\n    |- Try 18 + 12 = 30. Add 30 to the number set. Current number set: [30, 9], target: 36, just two numbers left.\n     |- Try 30 + 9 = 39. Evaluate 39 != 36, drop this branch.\n     |- Try 30 - 9 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 30 * 9 = 270. Evaluate 270 != 36, drop this branch.\n     |- Try 30 \/ 9 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 18 - 12 = 6. Add 6 to the number set. Current number set: [6, 9], target: 36, just two numbers left.\n     |- Try 9 + 6 = 15. Evaluate 15 != 36, drop this branch.\n     |- Try 9 - 6 = 3. Evaluate 3 != 36, drop this branch.\n     |- Try 9 * 6 = 54. Evaluate 54 != 36, drop this branch.\n     |- Try 9 \/ 6 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 * 12 = 216. Add 216 to the number set. Current number set: [216, 9], target: 36, just two numbers left.\n     |- Try 216 + 9 = 225. Evaluate 225 != 36, drop this branch.\n     |- Try 216 - 9 = 207. Evaluate 207 != 36, drop this branch.\n     |- Try 216 * 9 = 1944. Evaluate 1944 != 36, drop this branch.\n     |- Try 216 \/ 9 = 24. Evaluate 24 != 36, drop this branch.\n    |- Try 18 \/ 12 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 9) (numbers left: [12]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 12], target: 36, just two numbers left.\n     |- Try 27 + 12 = 39. Evaluate 39 != 36, drop this branch.\n     |- Try 27 - 12 = 15. Evaluate 15 != 36, drop this branch.\n     |- Try 27 * 12 = 324. Evaluate 324 != 36, drop this branch.\n     |- Try 27 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 12], target: 36, just two numbers left.\n     |- Try 12 + 9 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 12 - 9 = 3. Evaluate 3 != 36, drop this branch.\n     |- Try 12 * 9 = 108. Evaluate 108 != 36, drop this branch.\n     |- Try 12 \/ 9 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 12], target: 36, just two numbers left.\n     |- Try 162 + 12 = 174. Evaluate 174 != 36, drop this branch.\n     |- Try 162 - 12 = 150. Evaluate 150 != 36, drop this branch.\n     |- Try 162 * 12 = 1944. Evaluate 1944 != 36, drop this branch.\n     |- Try 162 \/ 12 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 12], target: 36, just two numbers left.\n     |- Try 12 + 2 = 14. Evaluate 14 != 36, drop this branch.\n     |- Try 12 - 2 = 10. Evaluate 10 != 36, drop this branch.\n     |- Try 12 * 2 = 24. Evaluate 24 != 36, drop this branch.\n     |- Try 12 \/ 2 = 6. Evaluate 6 != 36, drop this branch.\n   |- Pick two numbers (12, 9) (numbers left: [18]). Try possible operations.\n    |- Try 12 + 9 = 21. Add 21 to the number set. Current number set: [21, 18], target: 36, just two numbers left.\n     |- Try 21 + 18 = 39. Evaluate 39 != 36, drop this branch.\n     |- Try 21 - 18 = 3. Evaluate 3 != 36, drop this branch.\n     |- Try 21 * 18 = 378. Evaluate 378 != 36, drop this branch.\n     |- Try 21 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 12 - 9 = 3. Add 3 to the number set. Current number set: [3, 18], target: 36, just two numbers left.\n     |- Try 18 + 3 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 18 - 3 = 15. Evaluate 15 != 36, drop this branch.\n     |- Try 18 * 3 = 54. Evaluate 54 != 36, drop this branch.\n     |- Try 18 \/ 3 = 6. Evaluate 6 != 36, drop this branch.\n    |- Try 12 * 9 = 108. Add 108 to the number set. Current number set: [108, 18], target: 36, just two numbers left.\n     |- Try 108 + 18 = 126. Evaluate 126 != 36, drop this branch.\n     |- Try 108 - 18 = 90. Evaluate 90 != 36, drop this branch.\n     |- Try 108 * 18 = 1944. Evaluate 1944 != 36, drop this branch.\n     |- Try 108 \/ 18 = 6. Evaluate 6 != 36, drop this branch.\n    |- Try 12 \/ 9 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 13 - 5 = 8. Add 8 to the number set. Current number set: [8, 12, 9], target: 36. Options for choosing two numbers: [(8, 12), (8, 9), (12, 9)].\n   |- Pick two numbers (8, 12) (numbers left: [9]). Try possible operations.\n    |- Try 12 + 8 = 20. Add 20 to the number set. Current number set: [20, 9], target: 36, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 36, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 12 - 8 = 4. Add 4 to the number set. Current number set: [4, 9], target: 36, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 9 * 4 = 36\nThe step before: 12 - 8 = 4\nThe first step: 13 - 5 = 8\n\nOutput the solution in the required format:\n<Solution>\n13 - 5 = 8\n12 - 8 = 4\n9 * 4 = 36\n<\/Solution>\n","item":{"nums":[13,5,12,9],"solution":["13 - 5 = 8","12 - 8 = 4","9 * 4 = 36"],"target":36}}
+{"instance_id":"countdown_2k_74","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 43, 14, 8]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [4, 43, 14, 8], target: 33. Options for choosing two numbers: [(4, 43), (4, 14), (4, 8), (43, 14), (43, 8), (14, 8)].\n |- Pick two numbers (4, 43) (numbers left: [14, 8]). Try possible operations.\n  |- Try 43 + 4 = 47. Add 47 to the number set. Current number set: [47, 14, 8], target: 33. Options for choosing two numbers: [(47, 14), (47, 8), (14, 8)].\n   |- Pick two numbers (47, 14) (numbers left: [8]). Try possible operations.\n    |- Try 47 + 14 = 61. Add 61 to the number set. Current number set: [61, 8], target: 33, just two numbers left.\n     |- Try 61 + 8 = 69. Evaluate 69 != 33, drop this branch.\n     |- Try 61 - 8 = 53. Evaluate 53 != 33, drop this branch.\n     |- Try 61 * 8 = 488. Evaluate 488 != 33, drop this branch.\n     |- Try 61 \/ 8 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 47 - 14 = 33. Add 33 to the number set. Current number set: [33, 8], target: 33, just two numbers left.\n     |- Try 33 + 8 = 41. Evaluate 41 != 33, drop this branch.\n     |- Try 33 - 8 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 33 * 8 = 264. Evaluate 264 != 33, drop this branch.\n     |- Try 33 \/ 8 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 47 * 14 = 658. Add 658 to the number set. Current number set: [658, 8], target: 33, just two numbers left.\n     |- Try 658 + 8 = 666. Evaluate 666 != 33, drop this branch.\n     |- Try 658 - 8 = 650. Evaluate 650 != 33, drop this branch.\n     |- Try 658 * 8 = 5264. 5264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 658 \/ 8 = 82.2. 82.2 is a decimal, drop this branch.\n    |- Try 47 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (47, 8) (numbers left: [14]). Try possible operations.\n    |- Try 47 + 8 = 55. Add 55 to the number set. Current number set: [55, 14], target: 33, just two numbers left.\n     |- Try 55 + 14 = 69. Evaluate 69 != 33, drop this branch.\n     |- Try 55 - 14 = 41. Evaluate 41 != 33, drop this branch.\n     |- Try 55 * 14 = 770. Evaluate 770 != 33, drop this branch.\n     |- Try 55 \/ 14 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 47 - 8 = 39. Add 39 to the number set. Current number set: [39, 14], target: 33, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 33, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 33, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 47 * 8 = 376. Add 376 to the number set. Current number set: [376, 14], target: 33, just two numbers left.\n     |- Try 376 + 14 = 390. Evaluate 390 != 33, drop this branch.\n     |- Try 376 - 14 = 362. Evaluate 362 != 33, drop this branch.\n     |- Try 376 * 14 = 5264. 5264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 376 \/ 14 = 26.9. 26.9 is a decimal, drop this branch.\n    |- Try 47 \/ 8 = 5.9. 5.9 is a decimal, drop this branch.\n   |- Pick two numbers (14, 8) (numbers left: [47]). Try possible operations.\n    |- Try 14 + 8 = 22. Add 22 to the number set. Current number set: [22, 47], target: 33, just two numbers left.\n     |- Try 47 + 22 = 69. Evaluate 69 != 33, drop this branch.\n     |- Try 47 - 22 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 47 * 22 = 1034. Evaluate 1034 != 33, drop this branch.\n     |- Try 47 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 14 - 8 = 6. Add 6 to the number set. Current number set: [6, 47], target: 33, just two numbers left.\n     |- Try 47 + 6 = 53. Evaluate 53 != 33, drop this branch.\n     |- Try 47 - 6 = 41. Evaluate 41 != 33, drop this branch.\n     |- Try 47 * 6 = 282. Evaluate 282 != 33, drop this branch.\n     |- Try 47 \/ 6 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 14 * 8 = 112. Add 112 to the number set. Current number set: [112, 47], target: 33, just two numbers left.\n     |- Try 112 + 47 = 159. Evaluate 159 != 33, drop this branch.\n     |- Try 112 - 47 = 65. Evaluate 65 != 33, drop this branch.\n     |- Try 112 * 47 = 5264. 5264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 47 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 43 - 4 = 39. Add 39 to the number set. Current number set: [39, 14, 8], target: 33. Options for choosing two numbers: [(39, 14), (39, 8), (14, 8)].\n   |- Pick two numbers (39, 14) (numbers left: [8]). Try possible operations.\n    |- Try 39 + 14 = 53. Add 53 to the number set. Current number set: [53, 8], target: 33, just two numbers left.\n     |- Try 53 + 8 = 61. Evaluate 61 != 33, drop this branch.\n     |- Try 53 - 8 = 45. Evaluate 45 != 33, drop this branch.\n     |- Try 53 * 8 = 424. Evaluate 424 != 33, drop this branch.\n     |- Try 53 \/ 8 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 39 - 14 = 25. Add 25 to the number set. Current number set: [25, 8], target: 33, just two numbers left.\n     |- Try 25 + 8 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 25 + 8 = 33\nThe step before: 39 - 14 = 25\nThe first step: 43 - 4 = 39\n\nOutput the solution in the required format:\n<Solution>\n43 - 4 = 39\n39 - 14 = 25\n25 + 8 = 33\n<\/Solution>\n","item":{"nums":[4,43,14,8],"solution":["43 - 4 = 39","39 - 14 = 25","25 + 8 = 33"],"target":33}}
+{"instance_id":"countdown_2k_75","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [34, 44, 32, 36]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [34, 44, 32, 36], target: 14. Options for choosing two numbers: [(34, 44), (34, 32), (34, 36), (44, 32), (44, 36), (32, 36)].\n |- Pick two numbers (34, 44) (numbers left: [32, 36]). Try possible operations.\n  |- Try 44 + 34 = 78. Add 78 to the number set. Current number set: [78, 32, 36], target: 14. Options for choosing two numbers: [(78, 32), (78, 36), (32, 36)].\n   |- Pick two numbers (78, 32) (numbers left: [36]). Try possible operations.\n    |- Try 78 + 32 = 110. Add 110 to the number set. Current number set: [110, 36], target: 14, just two numbers left.\n     |- Try 110 + 36 = 146. Evaluate 146 != 14, drop this branch.\n     |- Try 110 - 36 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 110 * 36 = 3960. 3960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 36 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 78 - 32 = 46. Add 46 to the number set. Current number set: [46, 36], target: 14, just two numbers left.\n     |- Try 46 + 36 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 46 - 36 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 46 * 36 = 1656. Evaluate 1656 != 14, drop this branch.\n     |- Try 46 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 78 * 32 = 2496. 2496 exceeds the maximum intermediate result, drop this branch.\n    |- Try 78 \/ 32 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (78, 36) (numbers left: [32]). Try possible operations.\n    |- Try 78 + 36 = 114. Add 114 to the number set. Current number set: [114, 32], target: 14, just two numbers left.\n     |- Try 114 + 32 = 146. Evaluate 146 != 14, drop this branch.\n     |- Try 114 - 32 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 114 * 32 = 3648. 3648 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 32 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 78 - 36 = 42. Add 42 to the number set. Current number set: [42, 32], target: 14, just two numbers left.\n     |- Try 42 + 32 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 42 - 32 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 42 * 32 = 1344. Evaluate 1344 != 14, drop this branch.\n     |- Try 42 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 78 * 36 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n    |- Try 78 \/ 36 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (32, 36) (numbers left: [78]). Try possible operations.\n    |- Try 36 + 32 = 68. Add 68 to the number set. Current number set: [68, 78], target: 14, just two numbers left.\n     |- Try 78 + 68 = 146. Evaluate 146 != 14, drop this branch.\n     |- Try 78 - 68 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 78 * 68 = 5304. 5304 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 68 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 - 32 = 4. Add 4 to the number set. Current number set: [4, 78], target: 14, just two numbers left.\n     |- Try 78 + 4 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 78 - 4 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 78 * 4 = 312. Evaluate 312 != 14, drop this branch.\n     |- Try 78 \/ 4 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 36 * 32 = 1152. Add 1152 to the number set. Current number set: [1152, 78], target: 14, just two numbers left.\n     |- Try 1152 + 78 = 1230. Evaluate 1230 != 14, drop this branch.\n     |- Try 1152 - 78 = 1074. Evaluate 1074 != 14, drop this branch.\n     |- Try 1152 * 78 = 89856. 89856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1152 \/ 78 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 44 - 34 = 10. Add 10 to the number set. Current number set: [10, 32, 36], target: 14. Options for choosing two numbers: [(10, 32), (10, 36), (32, 36)].\n   |- Pick two numbers (10, 32) (numbers left: [36]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 36], target: 14, just two numbers left.\n     |- Try 42 + 36 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 42 - 36 = 6. Evaluate 6 != 14, drop this branch.\n     |- Try 42 * 36 = 1512. Evaluate 1512 != 14, drop this branch.\n     |- Try 42 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 36], target: 14, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 14, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 22 = 14\nThe step before: 32 - 10 = 22\nThe first step: 44 - 34 = 10\n\nOutput the solution in the required format:\n<Solution>\n44 - 34 = 10\n32 - 10 = 22\n36 - 22 = 14\n<\/Solution>\n","item":{"nums":[34,44,32,36],"solution":["44 - 34 = 10","32 - 10 = 22","36 - 22 = 14"],"target":14}}
+{"instance_id":"countdown_2k_76","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 5, 20, 5]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [47, 5, 20, 5], target: 13. Options for choosing two numbers: [(47, 5), (47, 20), (47, 5), (5, 20), (5, 5), (20, 5)].\n |- Pick two numbers (47, 5) (numbers left: [20, 5]). Try possible operations.\n  |- Try 47 + 5 = 52. Add 52 to the number set. Current number set: [52, 20, 5], target: 13. Options for choosing two numbers: [(52, 20), (52, 5), (20, 5)].\n   |- Pick two numbers (52, 20) (numbers left: [5]). Try possible operations.\n    |- Try 52 + 20 = 72. Add 72 to the number set. Current number set: [72, 5], target: 13, just two numbers left.\n     |- Try 72 + 5 = 77. Evaluate 77 != 13, drop this branch.\n     |- Try 72 - 5 = 67. Evaluate 67 != 13, drop this branch.\n     |- Try 72 * 5 = 360. Evaluate 360 != 13, drop this branch.\n     |- Try 72 \/ 5 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 52 - 20 = 32. Add 32 to the number set. Current number set: [32, 5], target: 13, just two numbers left.\n     |- Try 32 + 5 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 32 - 5 = 27. Evaluate 27 != 13, drop this branch.\n     |- Try 32 * 5 = 160. Evaluate 160 != 13, drop this branch.\n     |- Try 32 \/ 5 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 52 * 20 = 1040. Add 1040 to the number set. Current number set: [1040, 5], target: 13, just two numbers left.\n     |- Try 1040 + 5 = 1045. Evaluate 1045 != 13, drop this branch.\n     |- Try 1040 - 5 = 1035. Evaluate 1035 != 13, drop this branch.\n     |- Try 1040 * 5 = 5200. 5200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 5 = 208. Evaluate 208 != 13, drop this branch.\n    |- Try 52 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (52, 5) (numbers left: [20]). Try possible operations.\n    |- Try 52 + 5 = 57. Add 57 to the number set. Current number set: [57, 20], target: 13, just two numbers left.\n     |- Try 57 + 20 = 77. Evaluate 77 != 13, drop this branch.\n     |- Try 57 - 20 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 57 * 20 = 1140. Evaluate 1140 != 13, drop this branch.\n     |- Try 57 \/ 20 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 52 - 5 = 47. Add 47 to the number set. Current number set: [47, 20], target: 13, just two numbers left.\n     |- Try 47 + 20 = 67. Evaluate 67 != 13, drop this branch.\n     |- Try 47 - 20 = 27. Evaluate 27 != 13, drop this branch.\n     |- Try 47 * 20 = 940. Evaluate 940 != 13, drop this branch.\n     |- Try 47 \/ 20 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 52 * 5 = 260. Add 260 to the number set. Current number set: [260, 20], target: 13, just two numbers left.\n     |- Try 260 + 20 = 280. Evaluate 280 != 13, drop this branch.\n     |- Try 260 - 20 = 240. Evaluate 240 != 13, drop this branch.\n     |- Try 260 * 20 = 5200. 5200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 260 \/ 20 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 260 \/ 20 = 13\nThe step before: 52 * 5 = 260\nThe first step: 47 + 5 = 52\n\nOutput the solution in the required format:\n<Solution>\n47 + 5 = 52\n52 * 5 = 260\n260 \/ 20 = 13\n<\/Solution>\n","item":{"nums":[47,5,20,5],"solution":["47 + 5 = 52","52 * 5 = 260","260 \/ 20 = 13"],"target":13}}
+{"instance_id":"countdown_2k_77","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 39, 1, 41]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [42, 39, 1, 41], target: 37. Options for choosing two numbers: [(42, 39), (42, 1), (42, 41), (39, 1), (39, 41), (1, 41)].\n |- Pick two numbers (42, 39) (numbers left: [1, 41]). Try possible operations.\n  |- Try 42 + 39 = 81. Add 81 to the number set. Current number set: [81, 1, 41], target: 37. Options for choosing two numbers: [(81, 1), (81, 41), (1, 41)].\n   |- Pick two numbers (81, 1) (numbers left: [41]). Try possible operations.\n    |- Try 81 + 1 = 82. Add 82 to the number set. Current number set: [82, 41], target: 37, just two numbers left.\n     |- Try 82 + 41 = 123. Evaluate 123 != 37, drop this branch.\n     |- Try 82 - 41 = 41. Evaluate 41 != 37, drop this branch.\n     |- Try 82 * 41 = 3362. 3362 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 41 = 2. Evaluate 2 != 37, drop this branch.\n    |- Try 81 - 1 = 80. Add 80 to the number set. Current number set: [80, 41], target: 37, just two numbers left.\n     |- Try 80 + 41 = 121. Evaluate 121 != 37, drop this branch.\n     |- Try 80 - 41 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 80 * 41 = 3280. 3280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 81 * 1 = 81. Add 81 to the number set. Current number set: [81, 41], target: 37, just two numbers left.\n     |- Try 81 + 41 = 122. Evaluate 122 != 37, drop this branch.\n     |- Try 81 - 41 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 81 * 41 = 3321. 3321 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 81 \/ 1 = 81. Add 81 to the number set. Current number set: [81, 41], target: 37, just two numbers left.\n     |- Try 81 + 41 = 122. Evaluate 122 != 37, drop this branch.\n     |- Try 81 - 41 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 81 * 41 = 3321. 3321 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (81, 41) (numbers left: [1]). Try possible operations.\n    |- Try 81 + 41 = 122. Add 122 to the number set. Current number set: [122, 1], target: 37, just two numbers left.\n     |- Try 122 + 1 = 123. Evaluate 123 != 37, drop this branch.\n     |- Try 122 - 1 = 121. Evaluate 121 != 37, drop this branch.\n     |- Try 122 * 1 = 122. Evaluate 122 != 37, drop this branch.\n     |- Try 122 \/ 1 = 122. Evaluate 122 != 37, drop this branch.\n    |- Try 81 - 41 = 40. Add 40 to the number set. Current number set: [40, 1], target: 37, just two numbers left.\n     |- Try 40 + 1 = 41. Evaluate 41 != 37, drop this branch.\n     |- Try 40 - 1 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 40 * 1 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 40 \/ 1 = 40. Evaluate 40 != 37, drop this branch.\n    |- Try 81 * 41 = 3321. 3321 exceeds the maximum intermediate result, drop this branch.\n    |- Try 81 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (1, 41) (numbers left: [81]). Try possible operations.\n    |- Try 41 + 1 = 42. Add 42 to the number set. Current number set: [42, 81], target: 37, just two numbers left.\n     |- Try 81 + 42 = 123. Evaluate 123 != 37, drop this branch.\n     |- Try 81 - 42 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 81 * 42 = 3402. 3402 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 42 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 41 - 1 = 40. Add 40 to the number set. Current number set: [40, 81], target: 37, just two numbers left.\n     |- Try 81 + 40 = 121. Evaluate 121 != 37, drop this branch.\n     |- Try 81 - 40 = 41. Evaluate 41 != 37, drop this branch.\n     |- Try 81 * 40 = 3240. 3240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 40 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 41 * 1 = 41. Add 41 to the number set. Current number set: [41, 81], target: 37, just two numbers left.\n     |- Try 81 + 41 = 122. Evaluate 122 != 37, drop this branch.\n     |- Try 81 - 41 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 81 * 41 = 3321. 3321 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 41 \/ 1 = 41. Add 41 to the number set. Current number set: [41, 81], target: 37, just two numbers left.\n     |- Try 81 + 41 = 122. Evaluate 122 != 37, drop this branch.\n     |- Try 81 - 41 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 81 * 41 = 3321. 3321 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n  |- Try 42 - 39 = 3. Add 3 to the number set. Current number set: [3, 1, 41], target: 37. Options for choosing two numbers: [(3, 1), (3, 41), (1, 41)].\n   |- Pick two numbers (3, 1) (numbers left: [41]). Try possible operations.\n    |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 41], target: 37, just two numbers left.\n     |- Try 41 + 4 = 45. Evaluate 45 != 37, drop this branch.\n     |- Try 41 - 4 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 - 4 = 37\nThe step before: 3 + 1 = 4\nThe first step: 42 - 39 = 3\n\nOutput the solution in the required format:\n<Solution>\n42 - 39 = 3\n3 + 1 = 4\n41 - 4 = 37\n<\/Solution>\n","item":{"nums":[42,39,1,41],"solution":["42 - 39 = 3","3 + 1 = 4","41 - 4 = 37"],"target":37}}
+{"instance_id":"countdown_2k_78","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [36, 40, 48, 34]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [36, 40, 48, 34], target: 22. Options for choosing two numbers: [(36, 40), (36, 48), (36, 34), (40, 48), (40, 34), (48, 34)].\n |- Pick two numbers (36, 40) (numbers left: [48, 34]). Try possible operations.\n  |- Try 40 + 36 = 76. Add 76 to the number set. Current number set: [76, 48, 34], target: 22. Options for choosing two numbers: [(76, 48), (76, 34), (48, 34)].\n   |- Pick two numbers (76, 48) (numbers left: [34]). Try possible operations.\n    |- Try 76 + 48 = 124. Add 124 to the number set. Current number set: [124, 34], target: 22, just two numbers left.\n     |- Try 124 + 34 = 158. Evaluate 158 != 22, drop this branch.\n     |- Try 124 - 34 = 90. Evaluate 90 != 22, drop this branch.\n     |- Try 124 * 34 = 4216. 4216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 34 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 76 - 48 = 28. Add 28 to the number set. Current number set: [28, 34], target: 22, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 22, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 22, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 76 * 48 = 3648. 3648 exceeds the maximum intermediate result, drop this branch.\n    |- Try 76 \/ 48 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (76, 34) (numbers left: [48]). Try possible operations.\n    |- Try 76 + 34 = 110. Add 110 to the number set. Current number set: [110, 48], target: 22, just two numbers left.\n     |- Try 110 + 48 = 158. Evaluate 158 != 22, drop this branch.\n     |- Try 110 - 48 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 110 * 48 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 48 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 76 - 34 = 42. Add 42 to the number set. Current number set: [42, 48], target: 22, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 22, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 22, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 76 * 34 = 2584. 2584 exceeds the maximum intermediate result, drop this branch.\n    |- Try 76 \/ 34 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (48, 34) (numbers left: [76]). Try possible operations.\n    |- Try 48 + 34 = 82. Add 82 to the number set. Current number set: [82, 76], target: 22, just two numbers left.\n     |- Try 82 + 76 = 158. Evaluate 158 != 22, drop this branch.\n     |- Try 82 - 76 = 6. Evaluate 6 != 22, drop this branch.\n     |- Try 82 * 76 = 6232. 6232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 76 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 48 - 34 = 14. Add 14 to the number set. Current number set: [14, 76], target: 22, just two numbers left.\n     |- Try 76 + 14 = 90. Evaluate 90 != 22, drop this branch.\n     |- Try 76 - 14 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 76 * 14 = 1064. Evaluate 1064 != 22, drop this branch.\n     |- Try 76 \/ 14 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 48 * 34 = 1632. Add 1632 to the number set. Current number set: [1632, 76], target: 22, just two numbers left.\n     |- Try 1632 + 76 = 1708. Evaluate 1708 != 22, drop this branch.\n     |- Try 1632 - 76 = 1556. Evaluate 1556 != 22, drop this branch.\n     |- Try 1632 * 76 = 124032. 124032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1632 \/ 76 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 48 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 40 - 36 = 4. Add 4 to the number set. Current number set: [4, 48, 34], target: 22. Options for choosing two numbers: [(4, 48), (4, 34), (48, 34)].\n   |- Pick two numbers (4, 48) (numbers left: [34]). Try possible operations.\n    |- Try 48 + 4 = 52. Add 52 to the number set. Current number set: [52, 34], target: 22, just two numbers left.\n     |- Try 52 + 34 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 52 - 34 = 18. Evaluate 18 != 22, drop this branch.\n     |- Try 52 * 34 = 1768. Evaluate 1768 != 22, drop this branch.\n     |- Try 52 \/ 34 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 4 = 44. Add 44 to the number set. Current number set: [44, 34], target: 22, just two numbers left.\n     |- Try 44 + 34 = 78. Evaluate 78 != 22, drop this branch.\n     |- Try 44 - 34 = 10. Evaluate 10 != 22, drop this branch.\n     |- Try 44 * 34 = 1496. Evaluate 1496 != 22, drop this branch.\n     |- Try 44 \/ 34 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 * 4 = 192. Add 192 to the number set. Current number set: [192, 34], target: 22, just two numbers left.\n     |- Try 192 + 34 = 226. Evaluate 226 != 22, drop this branch.\n     |- Try 192 - 34 = 158. Evaluate 158 != 22, drop this branch.\n     |- Try 192 * 34 = 6528. 6528 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 34 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 48 \/ 4 = 12. Add 12 to the number set. Current number set: [12, 34], target: 22, just two numbers left.\n     |- Try 34 + 12 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 34 - 12 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 - 12 = 22\nThe step before: 48 \/ 4 = 12\nThe first step: 40 - 36 = 4\n\nOutput the solution in the required format:\n<Solution>\n40 - 36 = 4\n48 \/ 4 = 12\n34 - 12 = 22\n<\/Solution>\n","item":{"nums":[36,40,48,34],"solution":["40 - 36 = 4","48 \/ 4 = 12","34 - 12 = 22"],"target":22}}
+{"instance_id":"countdown_2k_79","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 29, 31, 2]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [20, 29, 31, 2], target: 11. Options for choosing two numbers: [(20, 29), (20, 31), (20, 2), (29, 31), (29, 2), (31, 2)].\n |- Pick two numbers (20, 29) (numbers left: [31, 2]). Try possible operations.\n  |- Try 29 + 20 = 49. Add 49 to the number set. Current number set: [49, 31, 2], target: 11. Options for choosing two numbers: [(49, 31), (49, 2), (31, 2)].\n   |- Pick two numbers (49, 31) (numbers left: [2]). Try possible operations.\n    |- Try 49 + 31 = 80. Add 80 to the number set. Current number set: [80, 2], target: 11, just two numbers left.\n     |- Try 80 + 2 = 82. Evaluate 82 != 11, drop this branch.\n     |- Try 80 - 2 = 78. Evaluate 78 != 11, drop this branch.\n     |- Try 80 * 2 = 160. Evaluate 160 != 11, drop this branch.\n     |- Try 80 \/ 2 = 40. Evaluate 40 != 11, drop this branch.\n    |- Try 49 - 31 = 18. Add 18 to the number set. Current number set: [18, 2], target: 11, just two numbers left.\n     |- Try 18 + 2 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 18 - 2 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 18 * 2 = 36. Evaluate 36 != 11, drop this branch.\n     |- Try 18 \/ 2 = 9. Evaluate 9 != 11, drop this branch.\n    |- Try 49 * 31 = 1519. Add 1519 to the number set. Current number set: [1519, 2], target: 11, just two numbers left.\n     |- Try 1519 + 2 = 1521. Evaluate 1521 != 11, drop this branch.\n     |- Try 1519 - 2 = 1517. Evaluate 1517 != 11, drop this branch.\n     |- Try 1519 * 2 = 3038. 3038 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1519 \/ 2 = 759.5. 759.5 is a decimal, drop this branch.\n    |- Try 49 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (49, 2) (numbers left: [31]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 31], target: 11, just two numbers left.\n     |- Try 51 + 31 = 82. Evaluate 82 != 11, drop this branch.\n     |- Try 51 - 31 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 51 * 31 = 1581. Evaluate 1581 != 11, drop this branch.\n     |- Try 51 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 31], target: 11, just two numbers left.\n     |- Try 47 + 31 = 78. Evaluate 78 != 11, drop this branch.\n     |- Try 47 - 31 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 47 * 31 = 1457. Evaluate 1457 != 11, drop this branch.\n     |- Try 47 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 31], target: 11, just two numbers left.\n     |- Try 98 + 31 = 129. Evaluate 129 != 11, drop this branch.\n     |- Try 98 - 31 = 67. Evaluate 67 != 11, drop this branch.\n     |- Try 98 * 31 = 3038. 3038 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 31 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 2) (numbers left: [49]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 49], target: 11, just two numbers left.\n     |- Try 49 + 33 = 82. Evaluate 82 != 11, drop this branch.\n     |- Try 49 - 33 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 49 * 33 = 1617. Evaluate 1617 != 11, drop this branch.\n     |- Try 49 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 31 - 2 = 29. Add 29 to the number set. Current number set: [29, 49], target: 11, just two numbers left.\n     |- Try 49 + 29 = 78. Evaluate 78 != 11, drop this branch.\n     |- Try 49 - 29 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 49 * 29 = 1421. Evaluate 1421 != 11, drop this branch.\n     |- Try 49 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 * 2 = 62. Add 62 to the number set. Current number set: [62, 49], target: 11, just two numbers left.\n     |- Try 62 + 49 = 111. Evaluate 111 != 11, drop this branch.\n     |- Try 62 - 49 = 13. Evaluate 13 != 11, drop this branch.\n     |- Try 62 * 49 = 3038. 3038 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 49 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n  |- Try 29 - 20 = 9. Add 9 to the number set. Current number set: [9, 31, 2], target: 11. Options for choosing two numbers: [(9, 31), (9, 2), (31, 2)].\n   |- Pick two numbers (9, 31) (numbers left: [2]). Try possible operations.\n    |- Try 31 + 9 = 40. Add 40 to the number set. Current number set: [40, 2], target: 11, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 11, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 11, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 11, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 11, drop this branch.\n    |- Try 31 - 9 = 22. Add 22 to the number set. Current number set: [22, 2], target: 11, just two numbers left.\n     |- Try 22 + 2 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 22 - 2 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 22 * 2 = 44. Evaluate 44 != 11, drop this branch.\n     |- Try 22 \/ 2 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 \/ 2 = 11\nThe step before: 31 - 9 = 22\nThe first step: 29 - 20 = 9\n\nOutput the solution in the required format:\n<Solution>\n29 - 20 = 9\n31 - 9 = 22\n22 \/ 2 = 11\n<\/Solution>\n","item":{"nums":[20,29,31,2],"solution":["29 - 20 = 9","31 - 9 = 22","22 \/ 2 = 11"],"target":11}}
+{"instance_id":"countdown_2k_80","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 36, 46, 2]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [30, 36, 46, 2], target: 42. Options for choosing two numbers: [(30, 36), (30, 46), (30, 2), (36, 46), (36, 2), (46, 2)].\n |- Pick two numbers (30, 36) (numbers left: [46, 2]). Try possible operations.\n  |- Try 36 + 30 = 66. Add 66 to the number set. Current number set: [66, 46, 2], target: 42. Options for choosing two numbers: [(66, 46), (66, 2), (46, 2)].\n   |- Pick two numbers (66, 46) (numbers left: [2]). Try possible operations.\n    |- Try 66 + 46 = 112. Add 112 to the number set. Current number set: [112, 2], target: 42, just two numbers left.\n     |- Try 112 + 2 = 114. Evaluate 114 != 42, drop this branch.\n     |- Try 112 - 2 = 110. Evaluate 110 != 42, drop this branch.\n     |- Try 112 * 2 = 224. Evaluate 224 != 42, drop this branch.\n     |- Try 112 \/ 2 = 56. Evaluate 56 != 42, drop this branch.\n    |- Try 66 - 46 = 20. Add 20 to the number set. Current number set: [20, 2], target: 42, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 42, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 42, drop this branch.\n    |- Try 66 * 46 = 3036. 3036 exceeds the maximum intermediate result, drop this branch.\n    |- Try 66 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (66, 2) (numbers left: [46]). Try possible operations.\n    |- Try 66 + 2 = 68. Add 68 to the number set. Current number set: [68, 46], target: 42, just two numbers left.\n     |- Try 68 + 46 = 114. Evaluate 114 != 42, drop this branch.\n     |- Try 68 - 46 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 68 * 46 = 3128. 3128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 46 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 66 - 2 = 64. Add 64 to the number set. Current number set: [64, 46], target: 42, just two numbers left.\n     |- Try 64 + 46 = 110. Evaluate 110 != 42, drop this branch.\n     |- Try 64 - 46 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 64 * 46 = 2944. 2944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 66 * 2 = 132. Add 132 to the number set. Current number set: [132, 46], target: 42, just two numbers left.\n     |- Try 132 + 46 = 178. Evaluate 178 != 42, drop this branch.\n     |- Try 132 - 46 = 86. Evaluate 86 != 42, drop this branch.\n     |- Try 132 * 46 = 6072. 6072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 46 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 66 \/ 2 = 33. Add 33 to the number set. Current number set: [33, 46], target: 42, just two numbers left.\n     |- Try 46 + 33 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 46 - 33 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 46 * 33 = 1518. Evaluate 1518 != 42, drop this branch.\n     |- Try 46 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (46, 2) (numbers left: [66]). Try possible operations.\n    |- Try 46 + 2 = 48. Add 48 to the number set. Current number set: [48, 66], target: 42, just two numbers left.\n     |- Try 66 + 48 = 114. Evaluate 114 != 42, drop this branch.\n     |- Try 66 - 48 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 66 * 48 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 48 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 - 2 = 44. Add 44 to the number set. Current number set: [44, 66], target: 42, just two numbers left.\n     |- Try 66 + 44 = 110. Evaluate 110 != 42, drop this branch.\n     |- Try 66 - 44 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 66 * 44 = 2904. 2904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 44 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 46 * 2 = 92. Add 92 to the number set. Current number set: [92, 66], target: 42, just two numbers left.\n     |- Try 92 + 66 = 158. Evaluate 158 != 42, drop this branch.\n     |- Try 92 - 66 = 26. Evaluate 26 != 42, drop this branch.\n     |- Try 92 * 66 = 6072. 6072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 66 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 \/ 2 = 23. Add 23 to the number set. Current number set: [23, 66], target: 42, just two numbers left.\n     |- Try 66 + 23 = 89. Evaluate 89 != 42, drop this branch.\n     |- Try 66 - 23 = 43. Evaluate 43 != 42, drop this branch.\n     |- Try 66 * 23 = 1518. Evaluate 1518 != 42, drop this branch.\n     |- Try 66 \/ 23 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 36 - 30 = 6. Add 6 to the number set. Current number set: [6, 46, 2], target: 42. Options for choosing two numbers: [(6, 46), (6, 2), (46, 2)].\n   |- Pick two numbers (6, 46) (numbers left: [2]). Try possible operations.\n    |- Try 46 + 6 = 52. Add 52 to the number set. Current number set: [52, 2], target: 42, just two numbers left.\n     |- Try 52 + 2 = 54. Evaluate 54 != 42, drop this branch.\n     |- Try 52 - 2 = 50. Evaluate 50 != 42, drop this branch.\n     |- Try 52 * 2 = 104. Evaluate 104 != 42, drop this branch.\n     |- Try 52 \/ 2 = 26. Evaluate 26 != 42, drop this branch.\n    |- Try 46 - 6 = 40. Add 40 to the number set. Current number set: [40, 2], target: 42, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 + 2 = 42\nThe step before: 46 - 6 = 40\nThe first step: 36 - 30 = 6\n\nOutput the solution in the required format:\n<Solution>\n36 - 30 = 6\n46 - 6 = 40\n40 + 2 = 42\n<\/Solution>\n","item":{"nums":[30,36,46,2],"solution":["36 - 30 = 6","46 - 6 = 40","40 + 2 = 42"],"target":42}}
+{"instance_id":"countdown_2k_81","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 25, 2, 36]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [17, 25, 2, 36], target: 12. Options for choosing two numbers: [(17, 25), (17, 2), (17, 36), (25, 2), (25, 36), (2, 36)].\n |- Pick two numbers (17, 25) (numbers left: [2, 36]). Try possible operations.\n  |- Try 25 + 17 = 42. Add 42 to the number set. Current number set: [42, 2, 36], target: 12. Options for choosing two numbers: [(42, 2), (42, 36), (2, 36)].\n   |- Pick two numbers (42, 2) (numbers left: [36]). Try possible operations.\n    |- Try 42 + 2 = 44. Add 44 to the number set. Current number set: [44, 36], target: 12, just two numbers left.\n     |- Try 44 + 36 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 44 - 36 = 8. Evaluate 8 != 12, drop this branch.\n     |- Try 44 * 36 = 1584. Evaluate 1584 != 12, drop this branch.\n     |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 - 2 = 40. Add 40 to the number set. Current number set: [40, 36], target: 12, just two numbers left.\n     |- Try 40 + 36 = 76. Evaluate 76 != 12, drop this branch.\n     |- Try 40 - 36 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 40 * 36 = 1440. Evaluate 1440 != 12, drop this branch.\n     |- Try 40 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 * 2 = 84. Add 84 to the number set. Current number set: [84, 36], target: 12, just two numbers left.\n     |- Try 84 + 36 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 84 - 36 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 84 * 36 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 36 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 42 \/ 2 = 21. Add 21 to the number set. Current number set: [21, 36], target: 12, just two numbers left.\n     |- Try 36 + 21 = 57. Evaluate 57 != 12, drop this branch.\n     |- Try 36 - 21 = 15. Evaluate 15 != 12, drop this branch.\n     |- Try 36 * 21 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 36 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (42, 36) (numbers left: [2]). Try possible operations.\n    |- Try 42 + 36 = 78. Add 78 to the number set. Current number set: [78, 2], target: 12, just two numbers left.\n     |- Try 78 + 2 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 78 - 2 = 76. Evaluate 76 != 12, drop this branch.\n     |- Try 78 * 2 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 78 \/ 2 = 39. Evaluate 39 != 12, drop this branch.\n    |- Try 42 - 36 = 6. Add 6 to the number set. Current number set: [6, 2], target: 12, just two numbers left.\n     |- Try 6 + 2 = 8. Evaluate 8 != 12, drop this branch.\n     |- Try 6 - 2 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 6 * 2 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 6 * 2 = 12\nThe step before: 42 - 36 = 6\nThe first step: 25 + 17 = 42\n\nOutput the solution in the required format:\n<Solution>\n25 + 17 = 42\n42 - 36 = 6\n6 * 2 = 12\n<\/Solution>\n","item":{"nums":[17,25,2,36],"solution":["25 + 17 = 42","42 - 36 = 6","6 * 2 = 12"],"target":12}}
+{"instance_id":"countdown_2k_82","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 47, 29, 19]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [20, 47, 29, 19], target: 21. Options for choosing two numbers: [(20, 47), (20, 29), (20, 19), (47, 29), (47, 19), (29, 19)].\n |- Pick two numbers (20, 47) (numbers left: [29, 19]). Try possible operations.\n  |- Try 47 + 20 = 67. Add 67 to the number set. Current number set: [67, 29, 19], target: 21. Options for choosing two numbers: [(67, 29), (67, 19), (29, 19)].\n   |- Pick two numbers (67, 29) (numbers left: [19]). Try possible operations.\n    |- Try 67 + 29 = 96. Add 96 to the number set. Current number set: [96, 19], target: 21, just two numbers left.\n     |- Try 96 + 19 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 96 - 19 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 96 * 19 = 1824. Evaluate 1824 != 21, drop this branch.\n     |- Try 96 \/ 19 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 67 - 29 = 38. Add 38 to the number set. Current number set: [38, 19], target: 21, just two numbers left.\n     |- Try 38 + 19 = 57. Evaluate 57 != 21, drop this branch.\n     |- Try 38 - 19 = 19. Evaluate 19 != 21, drop this branch.\n     |- Try 38 * 19 = 722. Evaluate 722 != 21, drop this branch.\n     |- Try 38 \/ 19 = 2. Evaluate 2 != 21, drop this branch.\n    |- Try 67 * 29 = 1943. Add 1943 to the number set. Current number set: [1943, 19], target: 21, just two numbers left.\n     |- Try 1943 + 19 = 1962. Evaluate 1962 != 21, drop this branch.\n     |- Try 1943 - 19 = 1924. Evaluate 1924 != 21, drop this branch.\n     |- Try 1943 * 19 = 36917. 36917 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1943 \/ 19 = 102.3. 102.3 is a decimal, drop this branch.\n    |- Try 67 \/ 29 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (67, 19) (numbers left: [29]). Try possible operations.\n    |- Try 67 + 19 = 86. Add 86 to the number set. Current number set: [86, 29], target: 21, just two numbers left.\n     |- Try 86 + 29 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 86 - 29 = 57. Evaluate 57 != 21, drop this branch.\n     |- Try 86 * 29 = 2494. 2494 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 29 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 67 - 19 = 48. Add 48 to the number set. Current number set: [48, 29], target: 21, just two numbers left.\n     |- Try 48 + 29 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 48 - 29 = 19. Evaluate 19 != 21, drop this branch.\n     |- Try 48 * 29 = 1392. Evaluate 1392 != 21, drop this branch.\n     |- Try 48 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 67 * 19 = 1273. Add 1273 to the number set. Current number set: [1273, 29], target: 21, just two numbers left.\n     |- Try 1273 + 29 = 1302. Evaluate 1302 != 21, drop this branch.\n     |- Try 1273 - 29 = 1244. Evaluate 1244 != 21, drop this branch.\n     |- Try 1273 * 29 = 36917. 36917 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1273 \/ 29 = 43.9. 43.9 is a decimal, drop this branch.\n    |- Try 67 \/ 19 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (29, 19) (numbers left: [67]). Try possible operations.\n    |- Try 29 + 19 = 48. Add 48 to the number set. Current number set: [48, 67], target: 21, just two numbers left.\n     |- Try 67 + 48 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 67 - 48 = 19. Evaluate 19 != 21, drop this branch.\n     |- Try 67 * 48 = 3216. 3216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 48 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 29 - 19 = 10. Add 10 to the number set. Current number set: [10, 67], target: 21, just two numbers left.\n     |- Try 67 + 10 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 67 - 10 = 57. Evaluate 57 != 21, drop this branch.\n     |- Try 67 * 10 = 670. Evaluate 670 != 21, drop this branch.\n     |- Try 67 \/ 10 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 29 * 19 = 551. Add 551 to the number set. Current number set: [551, 67], target: 21, just two numbers left.\n     |- Try 551 + 67 = 618. Evaluate 618 != 21, drop this branch.\n     |- Try 551 - 67 = 484. Evaluate 484 != 21, drop this branch.\n     |- Try 551 * 67 = 36917. 36917 exceeds the maximum intermediate result, drop this branch.\n     |- Try 551 \/ 67 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 29 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 47 - 20 = 27. Add 27 to the number set. Current number set: [27, 29, 19], target: 21. Options for choosing two numbers: [(27, 29), (27, 19), (29, 19)].\n   |- Pick two numbers (27, 29) (numbers left: [19]). Try possible operations.\n    |- Try 29 + 27 = 56. Add 56 to the number set. Current number set: [56, 19], target: 21, just two numbers left.\n     |- Try 56 + 19 = 75. Evaluate 75 != 21, drop this branch.\n     |- Try 56 - 19 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 56 * 19 = 1064. Evaluate 1064 != 21, drop this branch.\n     |- Try 56 \/ 19 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 29 - 27 = 2. Add 2 to the number set. Current number set: [2, 19], target: 21, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 + 2 = 21\nThe step before: 29 - 27 = 2\nThe first step: 47 - 20 = 27\n\nOutput the solution in the required format:\n<Solution>\n47 - 20 = 27\n29 - 27 = 2\n19 + 2 = 21\n<\/Solution>\n","item":{"nums":[20,47,29,19],"solution":["47 - 20 = 27","29 - 27 = 2","19 + 2 = 21"],"target":21}}
+{"instance_id":"countdown_2k_83","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [39, 46, 19, 28]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [39, 46, 19, 28], target: 16. Options for choosing two numbers: [(39, 46), (39, 19), (39, 28), (46, 19), (46, 28), (19, 28)].\n |- Pick two numbers (39, 46) (numbers left: [19, 28]). Try possible operations.\n  |- Try 46 + 39 = 85. Add 85 to the number set. Current number set: [85, 19, 28], target: 16. Options for choosing two numbers: [(85, 19), (85, 28), (19, 28)].\n   |- Pick two numbers (85, 19) (numbers left: [28]). Try possible operations.\n    |- Try 85 + 19 = 104. Add 104 to the number set. Current number set: [104, 28], target: 16, just two numbers left.\n     |- Try 104 + 28 = 132. Evaluate 132 != 16, drop this branch.\n     |- Try 104 - 28 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 104 * 28 = 2912. 2912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 28 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 85 - 19 = 66. Add 66 to the number set. Current number set: [66, 28], target: 16, just two numbers left.\n     |- Try 66 + 28 = 94. Evaluate 94 != 16, drop this branch.\n     |- Try 66 - 28 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 66 * 28 = 1848. Evaluate 1848 != 16, drop this branch.\n     |- Try 66 \/ 28 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 85 * 19 = 1615. Add 1615 to the number set. Current number set: [1615, 28], target: 16, just two numbers left.\n     |- Try 1615 + 28 = 1643. Evaluate 1643 != 16, drop this branch.\n     |- Try 1615 - 28 = 1587. Evaluate 1587 != 16, drop this branch.\n     |- Try 1615 * 28 = 45220. 45220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1615 \/ 28 = 57.7. 57.7 is a decimal, drop this branch.\n    |- Try 85 \/ 19 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (85, 28) (numbers left: [19]). Try possible operations.\n    |- Try 85 + 28 = 113. Add 113 to the number set. Current number set: [113, 19], target: 16, just two numbers left.\n     |- Try 113 + 19 = 132. Evaluate 132 != 16, drop this branch.\n     |- Try 113 - 19 = 94. Evaluate 94 != 16, drop this branch.\n     |- Try 113 * 19 = 2147. 2147 exceeds the maximum intermediate result, drop this branch.\n     |- Try 113 \/ 19 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 85 - 28 = 57. Add 57 to the number set. Current number set: [57, 19], target: 16, just two numbers left.\n     |- Try 57 + 19 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 57 - 19 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 57 * 19 = 1083. Evaluate 1083 != 16, drop this branch.\n     |- Try 57 \/ 19 = 3. Evaluate 3 != 16, drop this branch.\n    |- Try 85 * 28 = 2380. 2380 exceeds the maximum intermediate result, drop this branch.\n    |- Try 85 \/ 28 = 3.0. 3.0 is a decimal, drop this branch.\n   |- Pick two numbers (19, 28) (numbers left: [85]). Try possible operations.\n    |- Try 28 + 19 = 47. Add 47 to the number set. Current number set: [47, 85], target: 16, just two numbers left.\n     |- Try 85 + 47 = 132. Evaluate 132 != 16, drop this branch.\n     |- Try 85 - 47 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 85 * 47 = 3995. 3995 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 47 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 28 - 19 = 9. Add 9 to the number set. Current number set: [9, 85], target: 16, just two numbers left.\n     |- Try 85 + 9 = 94. Evaluate 94 != 16, drop this branch.\n     |- Try 85 - 9 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 85 * 9 = 765. Evaluate 765 != 16, drop this branch.\n     |- Try 85 \/ 9 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 28 * 19 = 532. Add 532 to the number set. Current number set: [532, 85], target: 16, just two numbers left.\n     |- Try 532 + 85 = 617. Evaluate 617 != 16, drop this branch.\n     |- Try 532 - 85 = 447. Evaluate 447 != 16, drop this branch.\n     |- Try 532 * 85 = 45220. 45220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 532 \/ 85 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 46 - 39 = 7. Add 7 to the number set. Current number set: [7, 19, 28], target: 16. Options for choosing two numbers: [(7, 19), (7, 28), (19, 28)].\n   |- Pick two numbers (7, 19) (numbers left: [28]). Try possible operations.\n    |- Try 19 + 7 = 26. Add 26 to the number set. Current number set: [26, 28], target: 16, just two numbers left.\n     |- Try 28 + 26 = 54. Evaluate 54 != 16, drop this branch.\n     |- Try 28 - 26 = 2. Evaluate 2 != 16, drop this branch.\n     |- Try 28 * 26 = 728. Evaluate 728 != 16, drop this branch.\n     |- Try 28 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 19 - 7 = 12. Add 12 to the number set. Current number set: [12, 28], target: 16, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 - 12 = 16\nThe step before: 19 - 7 = 12\nThe first step: 46 - 39 = 7\n\nOutput the solution in the required format:\n<Solution>\n46 - 39 = 7\n19 - 7 = 12\n28 - 12 = 16\n<\/Solution>\n","item":{"nums":[39,46,19,28],"solution":["46 - 39 = 7","19 - 7 = 12","28 - 12 = 16"],"target":16}}
+{"instance_id":"countdown_2k_84","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [40, 23, 9, 40]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [40, 23, 9, 40], target: 48. Options for choosing two numbers: [(40, 23), (40, 9), (40, 40), (23, 9), (23, 40), (9, 40)].\n |- Pick two numbers (40, 23) (numbers left: [9, 40]). Try possible operations.\n  |- Try 40 + 23 = 63. Add 63 to the number set. Current number set: [63, 9, 40], target: 48. Options for choosing two numbers: [(63, 9), (63, 40), (9, 40)].\n   |- Pick two numbers (63, 9) (numbers left: [40]). Try possible operations.\n    |- Try 63 + 9 = 72. Add 72 to the number set. Current number set: [72, 40], target: 48, just two numbers left.\n     |- Try 72 + 40 = 112. Evaluate 112 != 48, drop this branch.\n     |- Try 72 - 40 = 32. Evaluate 32 != 48, drop this branch.\n     |- Try 72 * 40 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 40 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 63 - 9 = 54. Add 54 to the number set. Current number set: [54, 40], target: 48, just two numbers left.\n     |- Try 54 + 40 = 94. Evaluate 94 != 48, drop this branch.\n     |- Try 54 - 40 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 54 * 40 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 63 * 9 = 567. Add 567 to the number set. Current number set: [567, 40], target: 48, just two numbers left.\n     |- Try 567 + 40 = 607. Evaluate 607 != 48, drop this branch.\n     |- Try 567 - 40 = 527. Evaluate 527 != 48, drop this branch.\n     |- Try 567 * 40 = 22680. 22680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 567 \/ 40 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 63 \/ 9 = 7. Add 7 to the number set. Current number set: [7, 40], target: 48, just two numbers left.\n     |- Try 40 + 7 = 47. Evaluate 47 != 48, drop this branch.\n     |- Try 40 - 7 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 40 * 7 = 280. Evaluate 280 != 48, drop this branch.\n     |- Try 40 \/ 7 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (63, 40) (numbers left: [9]). Try possible operations.\n    |- Try 63 + 40 = 103. Add 103 to the number set. Current number set: [103, 9], target: 48, just two numbers left.\n     |- Try 103 + 9 = 112. Evaluate 112 != 48, drop this branch.\n     |- Try 103 - 9 = 94. Evaluate 94 != 48, drop this branch.\n     |- Try 103 * 9 = 927. Evaluate 927 != 48, drop this branch.\n     |- Try 103 \/ 9 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 63 - 40 = 23. Add 23 to the number set. Current number set: [23, 9], target: 48, just two numbers left.\n     |- Try 23 + 9 = 32. Evaluate 32 != 48, drop this branch.\n     |- Try 23 - 9 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 23 * 9 = 207. Evaluate 207 != 48, drop this branch.\n     |- Try 23 \/ 9 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 63 * 40 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 40 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (9, 40) (numbers left: [63]). Try possible operations.\n    |- Try 40 + 9 = 49. Add 49 to the number set. Current number set: [49, 63], target: 48, just two numbers left.\n     |- Try 63 + 49 = 112. Evaluate 112 != 48, drop this branch.\n     |- Try 63 - 49 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 63 * 49 = 3087. 3087 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 49 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 40 - 9 = 31. Add 31 to the number set. Current number set: [31, 63], target: 48, just two numbers left.\n     |- Try 63 + 31 = 94. Evaluate 94 != 48, drop this branch.\n     |- Try 63 - 31 = 32. Evaluate 32 != 48, drop this branch.\n     |- Try 63 * 31 = 1953. Evaluate 1953 != 48, drop this branch.\n     |- Try 63 \/ 31 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 40 * 9 = 360. Add 360 to the number set. Current number set: [360, 63], target: 48, just two numbers left.\n     |- Try 360 + 63 = 423. Evaluate 423 != 48, drop this branch.\n     |- Try 360 - 63 = 297. Evaluate 297 != 48, drop this branch.\n     |- Try 360 * 63 = 22680. 22680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 63 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 40 \/ 9 = 4.4. 4.4 is a decimal, drop this branch.\n  |- Try 40 - 23 = 17. Add 17 to the number set. Current number set: [17, 9, 40], target: 48. Options for choosing two numbers: [(17, 9), (17, 40), (9, 40)].\n   |- Pick two numbers (17, 9) (numbers left: [40]). Try possible operations.\n    |- Try 17 + 9 = 26. Add 26 to the number set. Current number set: [26, 40], target: 48, just two numbers left.\n     |- Try 40 + 26 = 66. Evaluate 66 != 48, drop this branch.\n     |- Try 40 - 26 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 40 * 26 = 1040. Evaluate 1040 != 48, drop this branch.\n     |- Try 40 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 17 - 9 = 8. Add 8 to the number set. Current number set: [8, 40], target: 48, just two numbers left.\n     |- Try 40 + 8 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 + 8 = 48\nThe step before: 17 - 9 = 8\nThe first step: 40 - 23 = 17\n\nOutput the solution in the required format:\n<Solution>\n40 - 23 = 17\n17 - 9 = 8\n40 + 8 = 48\n<\/Solution>\n","item":{"nums":[40,23,9,40],"solution":["40 - 23 = 17","17 - 9 = 8","40 + 8 = 48"],"target":48}}
+{"instance_id":"countdown_2k_85","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [39, 37, 9, 33]\nTarget: 40","reference_output":"# Search Procedure\nInitial number set: [39, 37, 9, 33], target: 40. Options for choosing two numbers: [(39, 37), (39, 9), (39, 33), (37, 9), (37, 33), (9, 33)].\n |- Pick two numbers (39, 37) (numbers left: [9, 33]). Try possible operations.\n  |- Try 39 + 37 = 76. Add 76 to the number set. Current number set: [76, 9, 33], target: 40. Options for choosing two numbers: [(76, 9), (76, 33), (9, 33)].\n   |- Pick two numbers (76, 9) (numbers left: [33]). Try possible operations.\n    |- Try 76 + 9 = 85. Add 85 to the number set. Current number set: [85, 33], target: 40, just two numbers left.\n     |- Try 85 + 33 = 118. Evaluate 118 != 40, drop this branch.\n     |- Try 85 - 33 = 52. Evaluate 52 != 40, drop this branch.\n     |- Try 85 * 33 = 2805. 2805 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 33 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 76 - 9 = 67. Add 67 to the number set. Current number set: [67, 33], target: 40, just two numbers left.\n     |- Try 67 + 33 = 100. Evaluate 100 != 40, drop this branch.\n     |- Try 67 - 33 = 34. Evaluate 34 != 40, drop this branch.\n     |- Try 67 * 33 = 2211. 2211 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 33 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 76 * 9 = 684. Add 684 to the number set. Current number set: [684, 33], target: 40, just two numbers left.\n     |- Try 684 + 33 = 717. Evaluate 717 != 40, drop this branch.\n     |- Try 684 - 33 = 651. Evaluate 651 != 40, drop this branch.\n     |- Try 684 * 33 = 22572. 22572 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 33 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 76 \/ 9 = 8.4. 8.4 is a decimal, drop this branch.\n   |- Pick two numbers (76, 33) (numbers left: [9]). Try possible operations.\n    |- Try 76 + 33 = 109. Add 109 to the number set. Current number set: [109, 9], target: 40, just two numbers left.\n     |- Try 109 + 9 = 118. Evaluate 118 != 40, drop this branch.\n     |- Try 109 - 9 = 100. Evaluate 100 != 40, drop this branch.\n     |- Try 109 * 9 = 981. Evaluate 981 != 40, drop this branch.\n     |- Try 109 \/ 9 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 76 - 33 = 43. Add 43 to the number set. Current number set: [43, 9], target: 40, just two numbers left.\n     |- Try 43 + 9 = 52. Evaluate 52 != 40, drop this branch.\n     |- Try 43 - 9 = 34. Evaluate 34 != 40, drop this branch.\n     |- Try 43 * 9 = 387. Evaluate 387 != 40, drop this branch.\n     |- Try 43 \/ 9 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 76 * 33 = 2508. 2508 exceeds the maximum intermediate result, drop this branch.\n    |- Try 76 \/ 33 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (9, 33) (numbers left: [76]). Try possible operations.\n    |- Try 33 + 9 = 42. Add 42 to the number set. Current number set: [42, 76], target: 40, just two numbers left.\n     |- Try 76 + 42 = 118. Evaluate 118 != 40, drop this branch.\n     |- Try 76 - 42 = 34. Evaluate 34 != 40, drop this branch.\n     |- Try 76 * 42 = 3192. 3192 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 42 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 33 - 9 = 24. Add 24 to the number set. Current number set: [24, 76], target: 40, just two numbers left.\n     |- Try 76 + 24 = 100. Evaluate 100 != 40, drop this branch.\n     |- Try 76 - 24 = 52. Evaluate 52 != 40, drop this branch.\n     |- Try 76 * 24 = 1824. Evaluate 1824 != 40, drop this branch.\n     |- Try 76 \/ 24 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 33 * 9 = 297. Add 297 to the number set. Current number set: [297, 76], target: 40, just two numbers left.\n     |- Try 297 + 76 = 373. Evaluate 373 != 40, drop this branch.\n     |- Try 297 - 76 = 221. Evaluate 221 != 40, drop this branch.\n     |- Try 297 * 76 = 22572. 22572 exceeds the maximum intermediate result, drop this branch.\n     |- Try 297 \/ 76 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 39 - 37 = 2. Add 2 to the number set. Current number set: [2, 9, 33], target: 40. Options for choosing two numbers: [(2, 9), (2, 33), (9, 33)].\n   |- Pick two numbers (2, 9) (numbers left: [33]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 33], target: 40, just two numbers left.\n     |- Try 33 + 11 = 44. Evaluate 44 != 40, drop this branch.\n     |- Try 33 - 11 = 22. Evaluate 22 != 40, drop this branch.\n     |- Try 33 * 11 = 363. Evaluate 363 != 40, drop this branch.\n     |- Try 33 \/ 11 = 3. Evaluate 3 != 40, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 33], target: 40, just two numbers left.\n     |- Try 33 + 7 = 40. Evaluate 40 == 40, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 + 7 = 40\nThe step before: 9 - 2 = 7\nThe first step: 39 - 37 = 2\n\nOutput the solution in the required format:\n<Solution>\n39 - 37 = 2\n9 - 2 = 7\n33 + 7 = 40\n<\/Solution>\n","item":{"nums":[39,37,9,33],"solution":["39 - 37 = 2","9 - 2 = 7","33 + 7 = 40"],"target":40}}
+{"instance_id":"countdown_2k_86","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 8, 38, 39]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [32, 8, 38, 39], target: 23. Options for choosing two numbers: [(32, 8), (32, 38), (32, 39), (8, 38), (8, 39), (38, 39)].\n |- Pick two numbers (32, 8) (numbers left: [38, 39]). Try possible operations.\n  |- Try 32 + 8 = 40. Add 40 to the number set. Current number set: [40, 38, 39], target: 23. Options for choosing two numbers: [(40, 38), (40, 39), (38, 39)].\n   |- Pick two numbers (40, 38) (numbers left: [39]). Try possible operations.\n    |- Try 40 + 38 = 78. Add 78 to the number set. Current number set: [78, 39], target: 23, just two numbers left.\n     |- Try 78 + 39 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 78 - 39 = 39. Evaluate 39 != 23, drop this branch.\n     |- Try 78 * 39 = 3042. 3042 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 39 = 2. Evaluate 2 != 23, drop this branch.\n    |- Try 40 - 38 = 2. Add 2 to the number set. Current number set: [2, 39], target: 23, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 23, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 23, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 40 * 38 = 1520. Add 1520 to the number set. Current number set: [1520, 39], target: 23, just two numbers left.\n     |- Try 1520 + 39 = 1559. Evaluate 1559 != 23, drop this branch.\n     |- Try 1520 - 39 = 1481. Evaluate 1481 != 23, drop this branch.\n     |- Try 1520 * 39 = 59280. 59280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1520 \/ 39 = 39.0. 39.0 is a decimal, drop this branch.\n    |- Try 40 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (40, 39) (numbers left: [38]). Try possible operations.\n    |- Try 40 + 39 = 79. Add 79 to the number set. Current number set: [79, 38], target: 23, just two numbers left.\n     |- Try 79 + 38 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 79 - 38 = 41. Evaluate 41 != 23, drop this branch.\n     |- Try 79 * 38 = 3002. 3002 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 38 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 40 - 39 = 1. Add 1 to the number set. Current number set: [1, 38], target: 23, just two numbers left.\n     |- Try 38 + 1 = 39. Evaluate 39 != 23, drop this branch.\n     |- Try 38 - 1 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 38 * 1 = 38. Evaluate 38 != 23, drop this branch.\n     |- Try 38 \/ 1 = 38. Evaluate 38 != 23, drop this branch.\n    |- Try 40 * 39 = 1560. Add 1560 to the number set. Current number set: [1560, 38], target: 23, just two numbers left.\n     |- Try 1560 + 38 = 1598. Evaluate 1598 != 23, drop this branch.\n     |- Try 1560 - 38 = 1522. Evaluate 1522 != 23, drop this branch.\n     |- Try 1560 * 38 = 59280. 59280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1560 \/ 38 = 41.1. 41.1 is a decimal, drop this branch.\n    |- Try 40 \/ 39 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (38, 39) (numbers left: [40]). Try possible operations.\n    |- Try 39 + 38 = 77. Add 77 to the number set. Current number set: [77, 40], target: 23, just two numbers left.\n     |- Try 77 + 40 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 77 - 40 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 77 * 40 = 3080. 3080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 40 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 39 - 38 = 1. Add 1 to the number set. Current number set: [1, 40], target: 23, just two numbers left.\n     |- Try 40 + 1 = 41. Evaluate 41 != 23, drop this branch.\n     |- Try 40 - 1 = 39. Evaluate 39 != 23, drop this branch.\n     |- Try 40 * 1 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 40 \/ 1 = 40. Evaluate 40 != 23, drop this branch.\n    |- Try 39 * 38 = 1482. Add 1482 to the number set. Current number set: [1482, 40], target: 23, just two numbers left.\n     |- Try 1482 + 40 = 1522. Evaluate 1522 != 23, drop this branch.\n     |- Try 1482 - 40 = 1442. Evaluate 1442 != 23, drop this branch.\n     |- Try 1482 * 40 = 59280. 59280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1482 \/ 40 = 37.0. 37.0 is a decimal, drop this branch.\n    |- Try 39 \/ 38 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 32 - 8 = 24. Add 24 to the number set. Current number set: [24, 38, 39], target: 23. Options for choosing two numbers: [(24, 38), (24, 39), (38, 39)].\n   |- Pick two numbers (24, 38) (numbers left: [39]). Try possible operations.\n    |- Try 38 + 24 = 62. Add 62 to the number set. Current number set: [62, 39], target: 23, just two numbers left.\n     |- Try 62 + 39 = 101. Evaluate 101 != 23, drop this branch.\n     |- Try 62 - 39 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 62 - 39 = 23\nThe step before: 38 + 24 = 62\nThe first step: 32 - 8 = 24\n\nOutput the solution in the required format:\n<Solution>\n32 - 8 = 24\n38 + 24 = 62\n62 - 39 = 23\n<\/Solution>\n","item":{"nums":[32,8,38,39],"solution":["32 - 8 = 24","38 + 24 = 62","62 - 39 = 23"],"target":23}}
+{"instance_id":"countdown_2k_87","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 20, 26, 5]\nTarget: 39","reference_output":"# Search Procedure\nInitial number set: [12, 20, 26, 5], target: 39. Options for choosing two numbers: [(12, 20), (12, 26), (12, 5), (20, 26), (20, 5), (26, 5)].\n |- Pick two numbers (12, 20) (numbers left: [26, 5]). Try possible operations.\n  |- Try 20 + 12 = 32. Add 32 to the number set. Current number set: [32, 26, 5], target: 39. Options for choosing two numbers: [(32, 26), (32, 5), (26, 5)].\n   |- Pick two numbers (32, 26) (numbers left: [5]). Try possible operations.\n    |- Try 32 + 26 = 58. Add 58 to the number set. Current number set: [58, 5], target: 39, just two numbers left.\n     |- Try 58 + 5 = 63. Evaluate 63 != 39, drop this branch.\n     |- Try 58 - 5 = 53. Evaluate 53 != 39, drop this branch.\n     |- Try 58 * 5 = 290. Evaluate 290 != 39, drop this branch.\n     |- Try 58 \/ 5 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 32 - 26 = 6. Add 6 to the number set. Current number set: [6, 5], target: 39, just two numbers left.\n     |- Try 6 + 5 = 11. Evaluate 11 != 39, drop this branch.\n     |- Try 6 - 5 = 1. Evaluate 1 != 39, drop this branch.\n     |- Try 6 * 5 = 30. Evaluate 30 != 39, drop this branch.\n     |- Try 6 \/ 5 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 * 26 = 832. Add 832 to the number set. Current number set: [832, 5], target: 39, just two numbers left.\n     |- Try 832 + 5 = 837. Evaluate 837 != 39, drop this branch.\n     |- Try 832 - 5 = 827. Evaluate 827 != 39, drop this branch.\n     |- Try 832 * 5 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 832 \/ 5 = 166.4. 166.4 is a decimal, drop this branch.\n    |- Try 32 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (32, 5) (numbers left: [26]). Try possible operations.\n    |- Try 32 + 5 = 37. Add 37 to the number set. Current number set: [37, 26], target: 39, just two numbers left.\n     |- Try 37 + 26 = 63. Evaluate 63 != 39, drop this branch.\n     |- Try 37 - 26 = 11. Evaluate 11 != 39, drop this branch.\n     |- Try 37 * 26 = 962. Evaluate 962 != 39, drop this branch.\n     |- Try 37 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 - 5 = 27. Add 27 to the number set. Current number set: [27, 26], target: 39, just two numbers left.\n     |- Try 27 + 26 = 53. Evaluate 53 != 39, drop this branch.\n     |- Try 27 - 26 = 1. Evaluate 1 != 39, drop this branch.\n     |- Try 27 * 26 = 702. Evaluate 702 != 39, drop this branch.\n     |- Try 27 \/ 26 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 32 * 5 = 160. Add 160 to the number set. Current number set: [160, 26], target: 39, just two numbers left.\n     |- Try 160 + 26 = 186. Evaluate 186 != 39, drop this branch.\n     |- Try 160 - 26 = 134. Evaluate 134 != 39, drop this branch.\n     |- Try 160 * 26 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 26 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 32 \/ 5 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (26, 5) (numbers left: [32]). Try possible operations.\n    |- Try 26 + 5 = 31. Add 31 to the number set. Current number set: [31, 32], target: 39, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 39, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 39, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 39, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 26 - 5 = 21. Add 21 to the number set. Current number set: [21, 32], target: 39, just two numbers left.\n     |- Try 32 + 21 = 53. Evaluate 53 != 39, drop this branch.\n     |- Try 32 - 21 = 11. Evaluate 11 != 39, drop this branch.\n     |- Try 32 * 21 = 672. Evaluate 672 != 39, drop this branch.\n     |- Try 32 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 * 5 = 130. Add 130 to the number set. Current number set: [130, 32], target: 39, just two numbers left.\n     |- Try 130 + 32 = 162. Evaluate 162 != 39, drop this branch.\n     |- Try 130 - 32 = 98. Evaluate 98 != 39, drop this branch.\n     |- Try 130 * 32 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 32 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n  |- Try 20 - 12 = 8. Add 8 to the number set. Current number set: [8, 26, 5], target: 39. Options for choosing two numbers: [(8, 26), (8, 5), (26, 5)].\n   |- Pick two numbers (8, 26) (numbers left: [5]). Try possible operations.\n    |- Try 26 + 8 = 34. Add 34 to the number set. Current number set: [34, 5], target: 39, just two numbers left.\n     |- Try 34 + 5 = 39. Evaluate 39 == 39, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 5 = 39\nThe step before: 26 + 8 = 34\nThe first step: 20 - 12 = 8\n\nOutput the solution in the required format:\n<Solution>\n20 - 12 = 8\n26 + 8 = 34\n34 + 5 = 39\n<\/Solution>\n","item":{"nums":[12,20,26,5],"solution":["20 - 12 = 8","26 + 8 = 34","34 + 5 = 39"],"target":39}}
+{"instance_id":"countdown_2k_88","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 34, 3, 22]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [12, 34, 3, 22], target: 41. Options for choosing two numbers: [(12, 34), (12, 3), (12, 22), (34, 3), (34, 22), (3, 22)].\n |- Pick two numbers (12, 34) (numbers left: [3, 22]). Try possible operations.\n  |- Try 34 + 12 = 46. Add 46 to the number set. Current number set: [46, 3, 22], target: 41. Options for choosing two numbers: [(46, 3), (46, 22), (3, 22)].\n   |- Pick two numbers (46, 3) (numbers left: [22]). Try possible operations.\n    |- Try 46 + 3 = 49. Add 49 to the number set. Current number set: [49, 22], target: 41, just two numbers left.\n     |- Try 49 + 22 = 71. Evaluate 71 != 41, drop this branch.\n     |- Try 49 - 22 = 27. Evaluate 27 != 41, drop this branch.\n     |- Try 49 * 22 = 1078. Evaluate 1078 != 41, drop this branch.\n     |- Try 49 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 46 - 3 = 43. Add 43 to the number set. Current number set: [43, 22], target: 41, just two numbers left.\n     |- Try 43 + 22 = 65. Evaluate 65 != 41, drop this branch.\n     |- Try 43 - 22 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 43 * 22 = 946. Evaluate 946 != 41, drop this branch.\n     |- Try 43 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 46 * 3 = 138. Add 138 to the number set. Current number set: [138, 22], target: 41, just two numbers left.\n     |- Try 138 + 22 = 160. Evaluate 160 != 41, drop this branch.\n     |- Try 138 - 22 = 116. Evaluate 116 != 41, drop this branch.\n     |- Try 138 * 22 = 3036. 3036 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 22 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 46 \/ 3 = 15.3. 15.3 is a decimal, drop this branch.\n   |- Pick two numbers (46, 22) (numbers left: [3]). Try possible operations.\n    |- Try 46 + 22 = 68. Add 68 to the number set. Current number set: [68, 3], target: 41, just two numbers left.\n     |- Try 68 + 3 = 71. Evaluate 71 != 41, drop this branch.\n     |- Try 68 - 3 = 65. Evaluate 65 != 41, drop this branch.\n     |- Try 68 * 3 = 204. Evaluate 204 != 41, drop this branch.\n     |- Try 68 \/ 3 = 22.7. 22.7 is a decimal, drop this branch.\n    |- Try 46 - 22 = 24. Add 24 to the number set. Current number set: [24, 3], target: 41, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 41, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 24 * 3 = 72. Evaluate 72 != 41, drop this branch.\n     |- Try 24 \/ 3 = 8. Evaluate 8 != 41, drop this branch.\n    |- Try 46 * 22 = 1012. Add 1012 to the number set. Current number set: [1012, 3], target: 41, just two numbers left.\n     |- Try 1012 + 3 = 1015. Evaluate 1015 != 41, drop this branch.\n     |- Try 1012 - 3 = 1009. Evaluate 1009 != 41, drop this branch.\n     |- Try 1012 * 3 = 3036. 3036 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1012 \/ 3 = 337.3. 337.3 is a decimal, drop this branch.\n    |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (3, 22) (numbers left: [46]). Try possible operations.\n    |- Try 22 + 3 = 25. Add 25 to the number set. Current number set: [25, 46], target: 41, just two numbers left.\n     |- Try 46 + 25 = 71. Evaluate 71 != 41, drop this branch.\n     |- Try 46 - 25 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 46 * 25 = 1150. Evaluate 1150 != 41, drop this branch.\n     |- Try 46 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 22 - 3 = 19. Add 19 to the number set. Current number set: [19, 46], target: 41, just two numbers left.\n     |- Try 46 + 19 = 65. Evaluate 65 != 41, drop this branch.\n     |- Try 46 - 19 = 27. Evaluate 27 != 41, drop this branch.\n     |- Try 46 * 19 = 874. Evaluate 874 != 41, drop this branch.\n     |- Try 46 \/ 19 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 22 * 3 = 66. Add 66 to the number set. Current number set: [66, 46], target: 41, just two numbers left.\n     |- Try 66 + 46 = 112. Evaluate 112 != 41, drop this branch.\n     |- Try 66 - 46 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 66 * 46 = 3036. 3036 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 46 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 \/ 3 = 7.3. 7.3 is a decimal, drop this branch.\n  |- Try 34 - 12 = 22. Add 22 to the number set. Current number set: [22, 3, 22], target: 41. Options for choosing two numbers: [(22, 3), (22, 22), (3, 22)].\n   |- Pick two numbers (22, 3) (numbers left: [22]). Try possible operations.\n    |- Try 22 + 3 = 25. Add 25 to the number set. Current number set: [25, 22], target: 41, just two numbers left.\n     |- Try 25 + 22 = 47. Evaluate 47 != 41, drop this branch.\n     |- Try 25 - 22 = 3. Evaluate 3 != 41, drop this branch.\n     |- Try 25 * 22 = 550. Evaluate 550 != 41, drop this branch.\n     |- Try 25 \/ 22 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 - 3 = 19. Add 19 to the number set. Current number set: [19, 22], target: 41, just two numbers left.\n     |- Try 22 + 19 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 + 19 = 41\nThe step before: 22 - 3 = 19\nThe first step: 34 - 12 = 22\n\nOutput the solution in the required format:\n<Solution>\n34 - 12 = 22\n22 - 3 = 19\n22 + 19 = 41\n<\/Solution>\n","item":{"nums":[12,34,3,22],"solution":["34 - 12 = 22","22 - 3 = 19","22 + 19 = 41"],"target":41}}
+{"instance_id":"countdown_2k_89","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 35, 41, 23]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [7, 35, 41, 23], target: 10. Options for choosing two numbers: [(7, 35), (7, 41), (7, 23), (35, 41), (35, 23), (41, 23)].\n |- Pick two numbers (7, 35) (numbers left: [41, 23]). Try possible operations.\n  |- Try 35 + 7 = 42. Add 42 to the number set. Current number set: [42, 41, 23], target: 10. Options for choosing two numbers: [(42, 41), (42, 23), (41, 23)].\n   |- Pick two numbers (42, 41) (numbers left: [23]). Try possible operations.\n    |- Try 42 + 41 = 83. Add 83 to the number set. Current number set: [83, 23], target: 10, just two numbers left.\n     |- Try 83 + 23 = 106. Evaluate 106 != 10, drop this branch.\n     |- Try 83 - 23 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 83 * 23 = 1909. Evaluate 1909 != 10, drop this branch.\n     |- Try 83 \/ 23 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 42 - 41 = 1. Add 1 to the number set. Current number set: [1, 23], target: 10, just two numbers left.\n     |- Try 23 + 1 = 24. Evaluate 24 != 10, drop this branch.\n     |- Try 23 - 1 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 23 * 1 = 23. Evaluate 23 != 10, drop this branch.\n     |- Try 23 \/ 1 = 23. Evaluate 23 != 10, drop this branch.\n    |- Try 42 * 41 = 1722. Add 1722 to the number set. Current number set: [1722, 23], target: 10, just two numbers left.\n     |- Try 1722 + 23 = 1745. Evaluate 1745 != 10, drop this branch.\n     |- Try 1722 - 23 = 1699. Evaluate 1699 != 10, drop this branch.\n     |- Try 1722 * 23 = 39606. 39606 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1722 \/ 23 = 74.9. 74.9 is a decimal, drop this branch.\n    |- Try 42 \/ 41 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (42, 23) (numbers left: [41]). Try possible operations.\n    |- Try 42 + 23 = 65. Add 65 to the number set. Current number set: [65, 41], target: 10, just two numbers left.\n     |- Try 65 + 41 = 106. Evaluate 106 != 10, drop this branch.\n     |- Try 65 - 41 = 24. Evaluate 24 != 10, drop this branch.\n     |- Try 65 * 41 = 2665. 2665 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 41 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 42 - 23 = 19. Add 19 to the number set. Current number set: [19, 41], target: 10, just two numbers left.\n     |- Try 41 + 19 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 41 - 19 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 41 * 19 = 779. Evaluate 779 != 10, drop this branch.\n     |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 42 * 23 = 966. Add 966 to the number set. Current number set: [966, 41], target: 10, just two numbers left.\n     |- Try 966 + 41 = 1007. Evaluate 1007 != 10, drop this branch.\n     |- Try 966 - 41 = 925. Evaluate 925 != 10, drop this branch.\n     |- Try 966 * 41 = 39606. 39606 exceeds the maximum intermediate result, drop this branch.\n     |- Try 966 \/ 41 = 23.6. 23.6 is a decimal, drop this branch.\n    |- Try 42 \/ 23 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (41, 23) (numbers left: [42]). Try possible operations.\n    |- Try 41 + 23 = 64. Add 64 to the number set. Current number set: [64, 42], target: 10, just two numbers left.\n     |- Try 64 + 42 = 106. Evaluate 106 != 10, drop this branch.\n     |- Try 64 - 42 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 64 * 42 = 2688. 2688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 41 - 23 = 18. Add 18 to the number set. Current number set: [18, 42], target: 10, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 10, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 10, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 * 23 = 943. Add 943 to the number set. Current number set: [943, 42], target: 10, just two numbers left.\n     |- Try 943 + 42 = 985. Evaluate 985 != 10, drop this branch.\n     |- Try 943 - 42 = 901. Evaluate 901 != 10, drop this branch.\n     |- Try 943 * 42 = 39606. 39606 exceeds the maximum intermediate result, drop this branch.\n     |- Try 943 \/ 42 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 41 \/ 23 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 35 - 7 = 28. Add 28 to the number set. Current number set: [28, 41, 23], target: 10. Options for choosing two numbers: [(28, 41), (28, 23), (41, 23)].\n   |- Pick two numbers (28, 41) (numbers left: [23]). Try possible operations.\n    |- Try 41 + 28 = 69. Add 69 to the number set. Current number set: [69, 23], target: 10, just two numbers left.\n     |- Try 69 + 23 = 92. Evaluate 92 != 10, drop this branch.\n     |- Try 69 - 23 = 46. Evaluate 46 != 10, drop this branch.\n     |- Try 69 * 23 = 1587. Evaluate 1587 != 10, drop this branch.\n     |- Try 69 \/ 23 = 3. Evaluate 3 != 10, drop this branch.\n    |- Try 41 - 28 = 13. Add 13 to the number set. Current number set: [13, 23], target: 10, just two numbers left.\n     |- Try 23 + 13 = 36. Evaluate 36 != 10, drop this branch.\n     |- Try 23 - 13 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 - 13 = 10\nThe step before: 41 - 28 = 13\nThe first step: 35 - 7 = 28\n\nOutput the solution in the required format:\n<Solution>\n35 - 7 = 28\n41 - 28 = 13\n23 - 13 = 10\n<\/Solution>\n","item":{"nums":[7,35,41,23],"solution":["35 - 7 = 28","41 - 28 = 13","23 - 13 = 10"],"target":10}}
+{"instance_id":"countdown_2k_90","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 43, 5, 41]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [30, 43, 5, 41], target: 49. Options for choosing two numbers: [(30, 43), (30, 5), (30, 41), (43, 5), (43, 41), (5, 41)].\n |- Pick two numbers (30, 43) (numbers left: [5, 41]). Try possible operations.\n  |- Try 43 + 30 = 73. Add 73 to the number set. Current number set: [73, 5, 41], target: 49. Options for choosing two numbers: [(73, 5), (73, 41), (5, 41)].\n   |- Pick two numbers (73, 5) (numbers left: [41]). Try possible operations.\n    |- Try 73 + 5 = 78. Add 78 to the number set. Current number set: [78, 41], target: 49, just two numbers left.\n     |- Try 78 + 41 = 119. Evaluate 119 != 49, drop this branch.\n     |- Try 78 - 41 = 37. Evaluate 37 != 49, drop this branch.\n     |- Try 78 * 41 = 3198. 3198 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 41 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 73 - 5 = 68. Add 68 to the number set. Current number set: [68, 41], target: 49, just two numbers left.\n     |- Try 68 + 41 = 109. Evaluate 109 != 49, drop this branch.\n     |- Try 68 - 41 = 27. Evaluate 27 != 49, drop this branch.\n     |- Try 68 * 41 = 2788. 2788 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 41 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 73 * 5 = 365. Add 365 to the number set. Current number set: [365, 41], target: 49, just two numbers left.\n     |- Try 365 + 41 = 406. Evaluate 406 != 49, drop this branch.\n     |- Try 365 - 41 = 324. Evaluate 324 != 49, drop this branch.\n     |- Try 365 * 41 = 14965. 14965 exceeds the maximum intermediate result, drop this branch.\n     |- Try 365 \/ 41 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 73 \/ 5 = 14.6. 14.6 is a decimal, drop this branch.\n   |- Pick two numbers (73, 41) (numbers left: [5]). Try possible operations.\n    |- Try 73 + 41 = 114. Add 114 to the number set. Current number set: [114, 5], target: 49, just two numbers left.\n     |- Try 114 + 5 = 119. Evaluate 119 != 49, drop this branch.\n     |- Try 114 - 5 = 109. Evaluate 109 != 49, drop this branch.\n     |- Try 114 * 5 = 570. Evaluate 570 != 49, drop this branch.\n     |- Try 114 \/ 5 = 22.8. 22.8 is a decimal, drop this branch.\n    |- Try 73 - 41 = 32. Add 32 to the number set. Current number set: [32, 5], target: 49, just two numbers left.\n     |- Try 32 + 5 = 37. Evaluate 37 != 49, drop this branch.\n     |- Try 32 - 5 = 27. Evaluate 27 != 49, drop this branch.\n     |- Try 32 * 5 = 160. Evaluate 160 != 49, drop this branch.\n     |- Try 32 \/ 5 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 73 * 41 = 2993. 2993 exceeds the maximum intermediate result, drop this branch.\n    |- Try 73 \/ 41 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 41) (numbers left: [73]). Try possible operations.\n    |- Try 41 + 5 = 46. Add 46 to the number set. Current number set: [46, 73], target: 49, just two numbers left.\n     |- Try 73 + 46 = 119. Evaluate 119 != 49, drop this branch.\n     |- Try 73 - 46 = 27. Evaluate 27 != 49, drop this branch.\n     |- Try 73 * 46 = 3358. 3358 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 46 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 41 - 5 = 36. Add 36 to the number set. Current number set: [36, 73], target: 49, just two numbers left.\n     |- Try 73 + 36 = 109. Evaluate 109 != 49, drop this branch.\n     |- Try 73 - 36 = 37. Evaluate 37 != 49, drop this branch.\n     |- Try 73 * 36 = 2628. 2628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 36 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 41 * 5 = 205. Add 205 to the number set. Current number set: [205, 73], target: 49, just two numbers left.\n     |- Try 205 + 73 = 278. Evaluate 278 != 49, drop this branch.\n     |- Try 205 - 73 = 132. Evaluate 132 != 49, drop this branch.\n     |- Try 205 * 73 = 14965. 14965 exceeds the maximum intermediate result, drop this branch.\n     |- Try 205 \/ 73 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 41 \/ 5 = 8.2. 8.2 is a decimal, drop this branch.\n  |- Try 43 - 30 = 13. Add 13 to the number set. Current number set: [13, 5, 41], target: 49. Options for choosing two numbers: [(13, 5), (13, 41), (5, 41)].\n   |- Pick two numbers (13, 5) (numbers left: [41]). Try possible operations.\n    |- Try 13 + 5 = 18. Add 18 to the number set. Current number set: [18, 41], target: 49, just two numbers left.\n     |- Try 41 + 18 = 59. Evaluate 59 != 49, drop this branch.\n     |- Try 41 - 18 = 23. Evaluate 23 != 49, drop this branch.\n     |- Try 41 * 18 = 738. Evaluate 738 != 49, drop this branch.\n     |- Try 41 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 13 - 5 = 8. Add 8 to the number set. Current number set: [8, 41], target: 49, just two numbers left.\n     |- Try 41 + 8 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 + 8 = 49\nThe step before: 13 - 5 = 8\nThe first step: 43 - 30 = 13\n\nOutput the solution in the required format:\n<Solution>\n43 - 30 = 13\n13 - 5 = 8\n41 + 8 = 49\n<\/Solution>\n","item":{"nums":[30,43,5,41],"solution":["43 - 30 = 13","13 - 5 = 8","41 + 8 = 49"],"target":49}}
+{"instance_id":"countdown_2k_91","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 22, 47, 3]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [4, 22, 47, 3], target: 31. Options for choosing two numbers: [(4, 22), (4, 47), (4, 3), (22, 47), (22, 3), (47, 3)].\n |- Pick two numbers (4, 22) (numbers left: [47, 3]). Try possible operations.\n  |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 47, 3], target: 31. Options for choosing two numbers: [(26, 47), (26, 3), (47, 3)].\n   |- Pick two numbers (26, 47) (numbers left: [3]). Try possible operations.\n    |- Try 47 + 26 = 73. Add 73 to the number set. Current number set: [73, 3], target: 31, just two numbers left.\n     |- Try 73 + 3 = 76. Evaluate 76 != 31, drop this branch.\n     |- Try 73 - 3 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 73 * 3 = 219. Evaluate 219 != 31, drop this branch.\n     |- Try 73 \/ 3 = 24.3. 24.3 is a decimal, drop this branch.\n    |- Try 47 - 26 = 21. Add 21 to the number set. Current number set: [21, 3], target: 31, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 31, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 != 31, drop this branch.\n     |- Try 21 * 3 = 63. Evaluate 63 != 31, drop this branch.\n     |- Try 21 \/ 3 = 7. Evaluate 7 != 31, drop this branch.\n    |- Try 47 * 26 = 1222. Add 1222 to the number set. Current number set: [1222, 3], target: 31, just two numbers left.\n     |- Try 1222 + 3 = 1225. Evaluate 1225 != 31, drop this branch.\n     |- Try 1222 - 3 = 1219. Evaluate 1219 != 31, drop this branch.\n     |- Try 1222 * 3 = 3666. 3666 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1222 \/ 3 = 407.3. 407.3 is a decimal, drop this branch.\n    |- Try 47 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (26, 3) (numbers left: [47]). Try possible operations.\n    |- Try 26 + 3 = 29. Add 29 to the number set. Current number set: [29, 47], target: 31, just two numbers left.\n     |- Try 47 + 29 = 76. Evaluate 76 != 31, drop this branch.\n     |- Try 47 - 29 = 18. Evaluate 18 != 31, drop this branch.\n     |- Try 47 * 29 = 1363. Evaluate 1363 != 31, drop this branch.\n     |- Try 47 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 26 - 3 = 23. Add 23 to the number set. Current number set: [23, 47], target: 31, just two numbers left.\n     |- Try 47 + 23 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 47 - 23 = 24. Evaluate 24 != 31, drop this branch.\n     |- Try 47 * 23 = 1081. Evaluate 1081 != 31, drop this branch.\n     |- Try 47 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 26 * 3 = 78. Add 78 to the number set. Current number set: [78, 47], target: 31, just two numbers left.\n     |- Try 78 + 47 = 125. Evaluate 125 != 31, drop this branch.\n     |- Try 78 - 47 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 78 - 47 = 31\nThe step before: 26 * 3 = 78\nThe first step: 22 + 4 = 26\n\nOutput the solution in the required format:\n<Solution>\n22 + 4 = 26\n26 * 3 = 78\n78 - 47 = 31\n<\/Solution>\n","item":{"nums":[4,22,47,3],"solution":["22 + 4 = 26","26 * 3 = 78","78 - 47 = 31"],"target":31}}
+{"instance_id":"countdown_2k_92","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [11, 29, 16, 38]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [11, 29, 16, 38], target: 36. Options for choosing two numbers: [(11, 29), (11, 16), (11, 38), (29, 16), (29, 38), (16, 38)].\n |- Pick two numbers (11, 29) (numbers left: [16, 38]). Try possible operations.\n  |- Try 29 + 11 = 40. Add 40 to the number set. Current number set: [40, 16, 38], target: 36. Options for choosing two numbers: [(40, 16), (40, 38), (16, 38)].\n   |- Pick two numbers (40, 16) (numbers left: [38]). Try possible operations.\n    |- Try 40 + 16 = 56. Add 56 to the number set. Current number set: [56, 38], target: 36, just two numbers left.\n     |- Try 56 + 38 = 94. Evaluate 94 != 36, drop this branch.\n     |- Try 56 - 38 = 18. Evaluate 18 != 36, drop this branch.\n     |- Try 56 * 38 = 2128. 2128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 38 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 40 - 16 = 24. Add 24 to the number set. Current number set: [24, 38], target: 36, just two numbers left.\n     |- Try 38 + 24 = 62. Evaluate 62 != 36, drop this branch.\n     |- Try 38 - 24 = 14. Evaluate 14 != 36, drop this branch.\n     |- Try 38 * 24 = 912. Evaluate 912 != 36, drop this branch.\n     |- Try 38 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 40 * 16 = 640. Add 640 to the number set. Current number set: [640, 38], target: 36, just two numbers left.\n     |- Try 640 + 38 = 678. Evaluate 678 != 36, drop this branch.\n     |- Try 640 - 38 = 602. Evaluate 602 != 36, drop this branch.\n     |- Try 640 * 38 = 24320. 24320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 38 = 16.8. 16.8 is a decimal, drop this branch.\n    |- Try 40 \/ 16 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (40, 38) (numbers left: [16]). Try possible operations.\n    |- Try 40 + 38 = 78. Add 78 to the number set. Current number set: [78, 16], target: 36, just two numbers left.\n     |- Try 78 + 16 = 94. Evaluate 94 != 36, drop this branch.\n     |- Try 78 - 16 = 62. Evaluate 62 != 36, drop this branch.\n     |- Try 78 * 16 = 1248. Evaluate 1248 != 36, drop this branch.\n     |- Try 78 \/ 16 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 40 - 38 = 2. Add 2 to the number set. Current number set: [2, 16], target: 36, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 36, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 36, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 36, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 36, drop this branch.\n    |- Try 40 * 38 = 1520. Add 1520 to the number set. Current number set: [1520, 16], target: 36, just two numbers left.\n     |- Try 1520 + 16 = 1536. Evaluate 1536 != 36, drop this branch.\n     |- Try 1520 - 16 = 1504. Evaluate 1504 != 36, drop this branch.\n     |- Try 1520 * 16 = 24320. 24320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1520 \/ 16 = 95. Evaluate 95 != 36, drop this branch.\n    |- Try 40 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (16, 38) (numbers left: [40]). Try possible operations.\n    |- Try 38 + 16 = 54. Add 54 to the number set. Current number set: [54, 40], target: 36, just two numbers left.\n     |- Try 54 + 40 = 94. Evaluate 94 != 36, drop this branch.\n     |- Try 54 - 40 = 14. Evaluate 14 != 36, drop this branch.\n     |- Try 54 * 40 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 38 - 16 = 22. Add 22 to the number set. Current number set: [22, 40], target: 36, just two numbers left.\n     |- Try 40 + 22 = 62. Evaluate 62 != 36, drop this branch.\n     |- Try 40 - 22 = 18. Evaluate 18 != 36, drop this branch.\n     |- Try 40 * 22 = 880. Evaluate 880 != 36, drop this branch.\n     |- Try 40 \/ 22 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 38 * 16 = 608. Add 608 to the number set. Current number set: [608, 40], target: 36, just two numbers left.\n     |- Try 608 + 40 = 648. Evaluate 648 != 36, drop this branch.\n     |- Try 608 - 40 = 568. Evaluate 568 != 36, drop this branch.\n     |- Try 608 * 40 = 24320. 24320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 608 \/ 40 = 15.2. 15.2 is a decimal, drop this branch.\n    |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 29 - 11 = 18. Add 18 to the number set. Current number set: [18, 16, 38], target: 36. Options for choosing two numbers: [(18, 16), (18, 38), (16, 38)].\n   |- Pick two numbers (18, 16) (numbers left: [38]). Try possible operations.\n    |- Try 18 + 16 = 34. Add 34 to the number set. Current number set: [34, 38], target: 36, just two numbers left.\n     |- Try 38 + 34 = 72. Evaluate 72 != 36, drop this branch.\n     |- Try 38 - 34 = 4. Evaluate 4 != 36, drop this branch.\n     |- Try 38 * 34 = 1292. Evaluate 1292 != 36, drop this branch.\n     |- Try 38 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 18 - 16 = 2. Add 2 to the number set. Current number set: [2, 38], target: 36, just two numbers left.\n     |- Try 38 + 2 = 40. Evaluate 40 != 36, drop this branch.\n     |- Try 38 - 2 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 38 - 2 = 36\nThe step before: 18 - 16 = 2\nThe first step: 29 - 11 = 18\n\nOutput the solution in the required format:\n<Solution>\n29 - 11 = 18\n18 - 16 = 2\n38 - 2 = 36\n<\/Solution>\n","item":{"nums":[11,29,16,38],"solution":["29 - 11 = 18","18 - 16 = 2","38 - 2 = 36"],"target":36}}
+{"instance_id":"countdown_2k_93","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 42, 38, 19]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [46, 42, 38, 19], target: 15. Options for choosing two numbers: [(46, 42), (46, 38), (46, 19), (42, 38), (42, 19), (38, 19)].\n |- Pick two numbers (46, 42) (numbers left: [38, 19]). Try possible operations.\n  |- Try 46 + 42 = 88. Add 88 to the number set. Current number set: [88, 38, 19], target: 15. Options for choosing two numbers: [(88, 38), (88, 19), (38, 19)].\n   |- Pick two numbers (88, 38) (numbers left: [19]). Try possible operations.\n    |- Try 88 + 38 = 126. Add 126 to the number set. Current number set: [126, 19], target: 15, just two numbers left.\n     |- Try 126 + 19 = 145. Evaluate 145 != 15, drop this branch.\n     |- Try 126 - 19 = 107. Evaluate 107 != 15, drop this branch.\n     |- Try 126 * 19 = 2394. 2394 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 19 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 88 - 38 = 50. Add 50 to the number set. Current number set: [50, 19], target: 15, just two numbers left.\n     |- Try 50 + 19 = 69. Evaluate 69 != 15, drop this branch.\n     |- Try 50 - 19 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 50 * 19 = 950. Evaluate 950 != 15, drop this branch.\n     |- Try 50 \/ 19 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 88 * 38 = 3344. 3344 exceeds the maximum intermediate result, drop this branch.\n    |- Try 88 \/ 38 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (88, 19) (numbers left: [38]). Try possible operations.\n    |- Try 88 + 19 = 107. Add 107 to the number set. Current number set: [107, 38], target: 15, just two numbers left.\n     |- Try 107 + 38 = 145. Evaluate 145 != 15, drop this branch.\n     |- Try 107 - 38 = 69. Evaluate 69 != 15, drop this branch.\n     |- Try 107 * 38 = 4066. 4066 exceeds the maximum intermediate result, drop this branch.\n     |- Try 107 \/ 38 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 88 - 19 = 69. Add 69 to the number set. Current number set: [69, 38], target: 15, just two numbers left.\n     |- Try 69 + 38 = 107. Evaluate 107 != 15, drop this branch.\n     |- Try 69 - 38 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 69 * 38 = 2622. 2622 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 38 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 88 * 19 = 1672. Add 1672 to the number set. Current number set: [1672, 38], target: 15, just two numbers left.\n     |- Try 1672 + 38 = 1710. Evaluate 1710 != 15, drop this branch.\n     |- Try 1672 - 38 = 1634. Evaluate 1634 != 15, drop this branch.\n     |- Try 1672 * 38 = 63536. 63536 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1672 \/ 38 = 44. Evaluate 44 != 15, drop this branch.\n    |- Try 88 \/ 19 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (38, 19) (numbers left: [88]). Try possible operations.\n    |- Try 38 + 19 = 57. Add 57 to the number set. Current number set: [57, 88], target: 15, just two numbers left.\n     |- Try 88 + 57 = 145. Evaluate 145 != 15, drop this branch.\n     |- Try 88 - 57 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 88 * 57 = 5016. 5016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 57 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 38 - 19 = 19. Add 19 to the number set. Current number set: [19, 88], target: 15, just two numbers left.\n     |- Try 88 + 19 = 107. Evaluate 107 != 15, drop this branch.\n     |- Try 88 - 19 = 69. Evaluate 69 != 15, drop this branch.\n     |- Try 88 * 19 = 1672. Evaluate 1672 != 15, drop this branch.\n     |- Try 88 \/ 19 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 38 * 19 = 722. Add 722 to the number set. Current number set: [722, 88], target: 15, just two numbers left.\n     |- Try 722 + 88 = 810. Evaluate 810 != 15, drop this branch.\n     |- Try 722 - 88 = 634. Evaluate 634 != 15, drop this branch.\n     |- Try 722 * 88 = 63536. 63536 exceeds the maximum intermediate result, drop this branch.\n     |- Try 722 \/ 88 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 38 \/ 19 = 2. Add 2 to the number set. Current number set: [2, 88], target: 15, just two numbers left.\n     |- Try 88 + 2 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 88 - 2 = 86. Evaluate 86 != 15, drop this branch.\n     |- Try 88 * 2 = 176. Evaluate 176 != 15, drop this branch.\n     |- Try 88 \/ 2 = 44. Evaluate 44 != 15, drop this branch.\n  |- Try 46 - 42 = 4. Add 4 to the number set. Current number set: [4, 38, 19], target: 15. Options for choosing two numbers: [(4, 38), (4, 19), (38, 19)].\n   |- Pick two numbers (4, 38) (numbers left: [19]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 19], target: 15, just two numbers left.\n     |- Try 42 + 19 = 61. Evaluate 61 != 15, drop this branch.\n     |- Try 42 - 19 = 23. Evaluate 23 != 15, drop this branch.\n     |- Try 42 * 19 = 798. Evaluate 798 != 15, drop this branch.\n     |- Try 42 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 19], target: 15, just two numbers left.\n     |- Try 34 + 19 = 53. Evaluate 53 != 15, drop this branch.\n     |- Try 34 - 19 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 - 19 = 15\nThe step before: 38 - 4 = 34\nThe first step: 46 - 42 = 4\n\nOutput the solution in the required format:\n<Solution>\n46 - 42 = 4\n38 - 4 = 34\n34 - 19 = 15\n<\/Solution>\n","item":{"nums":[46,42,38,19],"solution":["46 - 42 = 4","38 - 4 = 34","34 - 19 = 15"],"target":15}}
+{"instance_id":"countdown_2k_94","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 24, 19, 14]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [42, 24, 19, 14], target: 13. Options for choosing two numbers: [(42, 24), (42, 19), (42, 14), (24, 19), (24, 14), (19, 14)].\n |- Pick two numbers (42, 24) (numbers left: [19, 14]). Try possible operations.\n  |- Try 42 + 24 = 66. Add 66 to the number set. Current number set: [66, 19, 14], target: 13. Options for choosing two numbers: [(66, 19), (66, 14), (19, 14)].\n   |- Pick two numbers (66, 19) (numbers left: [14]). Try possible operations.\n    |- Try 66 + 19 = 85. Add 85 to the number set. Current number set: [85, 14], target: 13, just two numbers left.\n     |- Try 85 + 14 = 99. Evaluate 99 != 13, drop this branch.\n     |- Try 85 - 14 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 85 * 14 = 1190. Evaluate 1190 != 13, drop this branch.\n     |- Try 85 \/ 14 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 66 - 19 = 47. Add 47 to the number set. Current number set: [47, 14], target: 13, just two numbers left.\n     |- Try 47 + 14 = 61. Evaluate 61 != 13, drop this branch.\n     |- Try 47 - 14 = 33. Evaluate 33 != 13, drop this branch.\n     |- Try 47 * 14 = 658. Evaluate 658 != 13, drop this branch.\n     |- Try 47 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 66 * 19 = 1254. Add 1254 to the number set. Current number set: [1254, 14], target: 13, just two numbers left.\n     |- Try 1254 + 14 = 1268. Evaluate 1268 != 13, drop this branch.\n     |- Try 1254 - 14 = 1240. Evaluate 1240 != 13, drop this branch.\n     |- Try 1254 * 14 = 17556. 17556 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1254 \/ 14 = 89.6. 89.6 is a decimal, drop this branch.\n    |- Try 66 \/ 19 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (66, 14) (numbers left: [19]). Try possible operations.\n    |- Try 66 + 14 = 80. Add 80 to the number set. Current number set: [80, 19], target: 13, just two numbers left.\n     |- Try 80 + 19 = 99. Evaluate 99 != 13, drop this branch.\n     |- Try 80 - 19 = 61. Evaluate 61 != 13, drop this branch.\n     |- Try 80 * 19 = 1520. Evaluate 1520 != 13, drop this branch.\n     |- Try 80 \/ 19 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 66 - 14 = 52. Add 52 to the number set. Current number set: [52, 19], target: 13, just two numbers left.\n     |- Try 52 + 19 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 52 - 19 = 33. Evaluate 33 != 13, drop this branch.\n     |- Try 52 * 19 = 988. Evaluate 988 != 13, drop this branch.\n     |- Try 52 \/ 19 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 66 * 14 = 924. Add 924 to the number set. Current number set: [924, 19], target: 13, just two numbers left.\n     |- Try 924 + 19 = 943. Evaluate 943 != 13, drop this branch.\n     |- Try 924 - 19 = 905. Evaluate 905 != 13, drop this branch.\n     |- Try 924 * 19 = 17556. 17556 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 19 = 48.6. 48.6 is a decimal, drop this branch.\n    |- Try 66 \/ 14 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 14) (numbers left: [66]). Try possible operations.\n    |- Try 19 + 14 = 33. Add 33 to the number set. Current number set: [33, 66], target: 13, just two numbers left.\n     |- Try 66 + 33 = 99. Evaluate 99 != 13, drop this branch.\n     |- Try 66 - 33 = 33. Evaluate 33 != 13, drop this branch.\n     |- Try 66 * 33 = 2178. 2178 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 33 = 2. Evaluate 2 != 13, drop this branch.\n    |- Try 19 - 14 = 5. Add 5 to the number set. Current number set: [5, 66], target: 13, just two numbers left.\n     |- Try 66 + 5 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 66 - 5 = 61. Evaluate 61 != 13, drop this branch.\n     |- Try 66 * 5 = 330. Evaluate 330 != 13, drop this branch.\n     |- Try 66 \/ 5 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 19 * 14 = 266. Add 266 to the number set. Current number set: [266, 66], target: 13, just two numbers left.\n     |- Try 266 + 66 = 332. Evaluate 332 != 13, drop this branch.\n     |- Try 266 - 66 = 200. Evaluate 200 != 13, drop this branch.\n     |- Try 266 * 66 = 17556. 17556 exceeds the maximum intermediate result, drop this branch.\n     |- Try 266 \/ 66 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 42 - 24 = 18. Add 18 to the number set. Current number set: [18, 19, 14], target: 13. Options for choosing two numbers: [(18, 19), (18, 14), (19, 14)].\n   |- Pick two numbers (18, 19) (numbers left: [14]). Try possible operations.\n    |- Try 19 + 18 = 37. Add 37 to the number set. Current number set: [37, 14], target: 13, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 13, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 13, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 19 - 18 = 1. Add 1 to the number set. Current number set: [1, 14], target: 13, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 != 13, drop this branch.\n     |- Try 14 - 1 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 14 - 1 = 13\nThe step before: 19 - 18 = 1\nThe first step: 42 - 24 = 18\n\nOutput the solution in the required format:\n<Solution>\n42 - 24 = 18\n19 - 18 = 1\n14 - 1 = 13\n<\/Solution>\n","item":{"nums":[42,24,19,14],"solution":["42 - 24 = 18","19 - 18 = 1","14 - 1 = 13"],"target":13}}
+{"instance_id":"countdown_2k_95","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [21, 15, 8, 21]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [21, 15, 8, 21], target: 42. Options for choosing two numbers: [(21, 15), (21, 8), (21, 21), (15, 8), (15, 21), (8, 21)].\n |- Pick two numbers (21, 15) (numbers left: [8, 21]). Try possible operations.\n  |- Try 21 + 15 = 36. Add 36 to the number set. Current number set: [36, 8, 21], target: 42. Options for choosing two numbers: [(36, 8), (36, 21), (8, 21)].\n   |- Pick two numbers (36, 8) (numbers left: [21]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 21], target: 42, just two numbers left.\n     |- Try 44 + 21 = 65. Evaluate 65 != 42, drop this branch.\n     |- Try 44 - 21 = 23. Evaluate 23 != 42, drop this branch.\n     |- Try 44 * 21 = 924. Evaluate 924 != 42, drop this branch.\n     |- Try 44 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 21], target: 42, just two numbers left.\n     |- Try 28 + 21 = 49. Evaluate 49 != 42, drop this branch.\n     |- Try 28 - 21 = 7. Evaluate 7 != 42, drop this branch.\n     |- Try 28 * 21 = 588. Evaluate 588 != 42, drop this branch.\n     |- Try 28 \/ 21 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 21], target: 42, just two numbers left.\n     |- Try 288 + 21 = 309. Evaluate 309 != 42, drop this branch.\n     |- Try 288 - 21 = 267. Evaluate 267 != 42, drop this branch.\n     |- Try 288 * 21 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 21 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (36, 21) (numbers left: [8]). Try possible operations.\n    |- Try 36 + 21 = 57. Add 57 to the number set. Current number set: [57, 8], target: 42, just two numbers left.\n     |- Try 57 + 8 = 65. Evaluate 65 != 42, drop this branch.\n     |- Try 57 - 8 = 49. Evaluate 49 != 42, drop this branch.\n     |- Try 57 * 8 = 456. Evaluate 456 != 42, drop this branch.\n     |- Try 57 \/ 8 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 36 - 21 = 15. Add 15 to the number set. Current number set: [15, 8], target: 42, just two numbers left.\n     |- Try 15 + 8 = 23. Evaluate 23 != 42, drop this branch.\n     |- Try 15 - 8 = 7. Evaluate 7 != 42, drop this branch.\n     |- Try 15 * 8 = 120. Evaluate 120 != 42, drop this branch.\n     |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 * 21 = 756. Add 756 to the number set. Current number set: [756, 8], target: 42, just two numbers left.\n     |- Try 756 + 8 = 764. Evaluate 764 != 42, drop this branch.\n     |- Try 756 - 8 = 748. Evaluate 748 != 42, drop this branch.\n     |- Try 756 * 8 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 756 \/ 8 = 94.5. 94.5 is a decimal, drop this branch.\n    |- Try 36 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (8, 21) (numbers left: [36]). Try possible operations.\n    |- Try 21 + 8 = 29. Add 29 to the number set. Current number set: [29, 36], target: 42, just two numbers left.\n     |- Try 36 + 29 = 65. Evaluate 65 != 42, drop this branch.\n     |- Try 36 - 29 = 7. Evaluate 7 != 42, drop this branch.\n     |- Try 36 * 29 = 1044. Evaluate 1044 != 42, drop this branch.\n     |- Try 36 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 21 - 8 = 13. Add 13 to the number set. Current number set: [13, 36], target: 42, just two numbers left.\n     |- Try 36 + 13 = 49. Evaluate 49 != 42, drop this branch.\n     |- Try 36 - 13 = 23. Evaluate 23 != 42, drop this branch.\n     |- Try 36 * 13 = 468. Evaluate 468 != 42, drop this branch.\n     |- Try 36 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 21 * 8 = 168. Add 168 to the number set. Current number set: [168, 36], target: 42, just two numbers left.\n     |- Try 168 + 36 = 204. Evaluate 204 != 42, drop this branch.\n     |- Try 168 - 36 = 132. Evaluate 132 != 42, drop this branch.\n     |- Try 168 * 36 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 36 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 21 - 15 = 6. Add 6 to the number set. Current number set: [6, 8, 21], target: 42. Options for choosing two numbers: [(6, 8), (6, 21), (8, 21)].\n   |- Pick two numbers (6, 8) (numbers left: [21]). Try possible operations.\n    |- Try 8 + 6 = 14. Add 14 to the number set. Current number set: [14, 21], target: 42, just two numbers left.\n     |- Try 21 + 14 = 35. Evaluate 35 != 42, drop this branch.\n     |- Try 21 - 14 = 7. Evaluate 7 != 42, drop this branch.\n     |- Try 21 * 14 = 294. Evaluate 294 != 42, drop this branch.\n     |- Try 21 \/ 14 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 8 - 6 = 2. Add 2 to the number set. Current number set: [2, 21], target: 42, just two numbers left.\n     |- Try 21 + 2 = 23. Evaluate 23 != 42, drop this branch.\n     |- Try 21 - 2 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 21 * 2 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 * 2 = 42\nThe step before: 8 - 6 = 2\nThe first step: 21 - 15 = 6\n\nOutput the solution in the required format:\n<Solution>\n21 - 15 = 6\n8 - 6 = 2\n21 * 2 = 42\n<\/Solution>\n","item":{"nums":[21,15,8,21],"solution":["21 - 15 = 6","8 - 6 = 2","21 * 2 = 42"],"target":42}}
+{"instance_id":"countdown_2k_96","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 9, 8, 30]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [18, 9, 8, 30], target: 13. Options for choosing two numbers: [(18, 9), (18, 8), (18, 30), (9, 8), (9, 30), (8, 30)].\n |- Pick two numbers (18, 9) (numbers left: [8, 30]). Try possible operations.\n  |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 8, 30], target: 13. Options for choosing two numbers: [(27, 8), (27, 30), (8, 30)].\n   |- Pick two numbers (27, 8) (numbers left: [30]). Try possible operations.\n    |- Try 27 + 8 = 35. Add 35 to the number set. Current number set: [35, 30], target: 13, just two numbers left.\n     |- Try 35 + 30 = 65. Evaluate 65 != 13, drop this branch.\n     |- Try 35 - 30 = 5. Evaluate 5 != 13, drop this branch.\n     |- Try 35 * 30 = 1050. Evaluate 1050 != 13, drop this branch.\n     |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 27 - 8 = 19. Add 19 to the number set. Current number set: [19, 30], target: 13, just two numbers left.\n     |- Try 30 + 19 = 49. Evaluate 49 != 13, drop this branch.\n     |- Try 30 - 19 = 11. Evaluate 11 != 13, drop this branch.\n     |- Try 30 * 19 = 570. Evaluate 570 != 13, drop this branch.\n     |- Try 30 \/ 19 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 27 * 8 = 216. Add 216 to the number set. Current number set: [216, 30], target: 13, just two numbers left.\n     |- Try 216 + 30 = 246. Evaluate 246 != 13, drop this branch.\n     |- Try 216 - 30 = 186. Evaluate 186 != 13, drop this branch.\n     |- Try 216 * 30 = 6480. 6480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 216 \/ 30 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 27 \/ 8 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (27, 30) (numbers left: [8]). Try possible operations.\n    |- Try 30 + 27 = 57. Add 57 to the number set. Current number set: [57, 8], target: 13, just two numbers left.\n     |- Try 57 + 8 = 65. Evaluate 65 != 13, drop this branch.\n     |- Try 57 - 8 = 49. Evaluate 49 != 13, drop this branch.\n     |- Try 57 * 8 = 456. Evaluate 456 != 13, drop this branch.\n     |- Try 57 \/ 8 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 30 - 27 = 3. Add 3 to the number set. Current number set: [3, 8], target: 13, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 13, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 13, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 13, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 30 * 27 = 810. Add 810 to the number set. Current number set: [810, 8], target: 13, just two numbers left.\n     |- Try 810 + 8 = 818. Evaluate 818 != 13, drop this branch.\n     |- Try 810 - 8 = 802. Evaluate 802 != 13, drop this branch.\n     |- Try 810 * 8 = 6480. 6480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 810 \/ 8 = 101.2. 101.2 is a decimal, drop this branch.\n    |- Try 30 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (8, 30) (numbers left: [27]). Try possible operations.\n    |- Try 30 + 8 = 38. Add 38 to the number set. Current number set: [38, 27], target: 13, just two numbers left.\n     |- Try 38 + 27 = 65. Evaluate 65 != 13, drop this branch.\n     |- Try 38 - 27 = 11. Evaluate 11 != 13, drop this branch.\n     |- Try 38 * 27 = 1026. Evaluate 1026 != 13, drop this branch.\n     |- Try 38 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 - 8 = 22. Add 22 to the number set. Current number set: [22, 27], target: 13, just two numbers left.\n     |- Try 27 + 22 = 49. Evaluate 49 != 13, drop this branch.\n     |- Try 27 - 22 = 5. Evaluate 5 != 13, drop this branch.\n     |- Try 27 * 22 = 594. Evaluate 594 != 13, drop this branch.\n     |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 * 8 = 240. Add 240 to the number set. Current number set: [240, 27], target: 13, just two numbers left.\n     |- Try 240 + 27 = 267. Evaluate 267 != 13, drop this branch.\n     |- Try 240 - 27 = 213. Evaluate 213 != 13, drop this branch.\n     |- Try 240 * 27 = 6480. 6480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 27 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n  |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 8, 30], target: 13. Options for choosing two numbers: [(9, 8), (9, 30), (8, 30)].\n   |- Pick two numbers (9, 8) (numbers left: [30]). Try possible operations.\n    |- Try 9 + 8 = 17. Add 17 to the number set. Current number set: [17, 30], target: 13, just two numbers left.\n     |- Try 30 + 17 = 47. Evaluate 47 != 13, drop this branch.\n     |- Try 30 - 17 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 - 17 = 13\nThe step before: 9 + 8 = 17\nThe first step: 18 - 9 = 9\n\nOutput the solution in the required format:\n<Solution>\n18 - 9 = 9\n9 + 8 = 17\n30 - 17 = 13\n<\/Solution>\n","item":{"nums":[18,9,8,30],"solution":["18 - 9 = 9","9 + 8 = 17","30 - 17 = 13"],"target":13}}
+{"instance_id":"countdown_2k_97","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 16, 6, 36]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [32, 16, 6, 36], target: 42. Options for choosing two numbers: [(32, 16), (32, 6), (32, 36), (16, 6), (16, 36), (6, 36)].\n |- Pick two numbers (32, 16) (numbers left: [6, 36]). Try possible operations.\n  |- Try 32 + 16 = 48. Add 48 to the number set. Current number set: [48, 6, 36], target: 42. Options for choosing two numbers: [(48, 6), (48, 36), (6, 36)].\n   |- Pick two numbers (48, 6) (numbers left: [36]). Try possible operations.\n    |- Try 48 + 6 = 54. Add 54 to the number set. Current number set: [54, 36], target: 42, just two numbers left.\n     |- Try 54 + 36 = 90. Evaluate 90 != 42, drop this branch.\n     |- Try 54 - 36 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 54 * 36 = 1944. Evaluate 1944 != 42, drop this branch.\n     |- Try 54 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 6 = 42. Add 42 to the number set. Current number set: [42, 36], target: 42, just two numbers left.\n     |- Try 42 + 36 = 78. Evaluate 78 != 42, drop this branch.\n     |- Try 42 - 36 = 6. Evaluate 6 != 42, drop this branch.\n     |- Try 42 * 36 = 1512. Evaluate 1512 != 42, drop this branch.\n     |- Try 42 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 6 = 288. Add 288 to the number set. Current number set: [288, 36], target: 42, just two numbers left.\n     |- Try 288 + 36 = 324. Evaluate 324 != 42, drop this branch.\n     |- Try 288 - 36 = 252. Evaluate 252 != 42, drop this branch.\n     |- Try 288 * 36 = 10368. 10368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 36 = 8. Evaluate 8 != 42, drop this branch.\n    |- Try 48 \/ 6 = 8. Add 8 to the number set. Current number set: [8, 36], target: 42, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 42, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 42, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (48, 36) (numbers left: [6]). Try possible operations.\n    |- Try 48 + 36 = 84. Add 84 to the number set. Current number set: [84, 6], target: 42, just two numbers left.\n     |- Try 84 + 6 = 90. Evaluate 90 != 42, drop this branch.\n     |- Try 84 - 6 = 78. Evaluate 78 != 42, drop this branch.\n     |- Try 84 * 6 = 504. Evaluate 504 != 42, drop this branch.\n     |- Try 84 \/ 6 = 14. Evaluate 14 != 42, drop this branch.\n    |- Try 48 - 36 = 12. Add 12 to the number set. Current number set: [12, 6], target: 42, just two numbers left.\n     |- Try 12 + 6 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 12 - 6 = 6. Evaluate 6 != 42, drop this branch.\n     |- Try 12 * 6 = 72. Evaluate 72 != 42, drop this branch.\n     |- Try 12 \/ 6 = 2. Evaluate 2 != 42, drop this branch.\n    |- Try 48 * 36 = 1728. Add 1728 to the number set. Current number set: [1728, 6], target: 42, just two numbers left.\n     |- Try 1728 + 6 = 1734. Evaluate 1734 != 42, drop this branch.\n     |- Try 1728 - 6 = 1722. Evaluate 1722 != 42, drop this branch.\n     |- Try 1728 * 6 = 10368. 10368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1728 \/ 6 = 288. Evaluate 288 != 42, drop this branch.\n    |- Try 48 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 36) (numbers left: [48]). Try possible operations.\n    |- Try 36 + 6 = 42. Add 42 to the number set. Current number set: [42, 48], target: 42, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 42, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 42, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 - 6 = 30. Add 30 to the number set. Current number set: [30, 48], target: 42, just two numbers left.\n     |- Try 48 + 30 = 78. Evaluate 78 != 42, drop this branch.\n     |- Try 48 - 30 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 48 * 30 = 1440. Evaluate 1440 != 42, drop this branch.\n     |- Try 48 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 * 6 = 216. Add 216 to the number set. Current number set: [216, 48], target: 42, just two numbers left.\n     |- Try 216 + 48 = 264. Evaluate 264 != 42, drop this branch.\n     |- Try 216 - 48 = 168. Evaluate 168 != 42, drop this branch.\n     |- Try 216 * 48 = 10368. 10368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 216 \/ 48 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 36 \/ 6 = 6. Add 6 to the number set. Current number set: [6, 48], target: 42, just two numbers left.\n     |- Try 48 + 6 = 54. Evaluate 54 != 42, drop this branch.\n     |- Try 48 - 6 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 6 = 42\nThe step before: 36 \/ 6 = 6\nThe first step: 32 + 16 = 48\n\nOutput the solution in the required format:\n<Solution>\n32 + 16 = 48\n36 \/ 6 = 6\n48 - 6 = 42\n<\/Solution>\n","item":{"nums":[32,16,6,36],"solution":["32 + 16 = 48","36 \/ 6 = 6","48 - 6 = 42"],"target":42}}
+{"instance_id":"countdown_2k_98","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 44, 24, 4]\nTarget: 39","reference_output":"# Search Procedure\nInitial number set: [33, 44, 24, 4], target: 39. Options for choosing two numbers: [(33, 44), (33, 24), (33, 4), (44, 24), (44, 4), (24, 4)].\n |- Pick two numbers (33, 44) (numbers left: [24, 4]). Try possible operations.\n  |- Try 44 + 33 = 77. Add 77 to the number set. Current number set: [77, 24, 4], target: 39. Options for choosing two numbers: [(77, 24), (77, 4), (24, 4)].\n   |- Pick two numbers (77, 24) (numbers left: [4]). Try possible operations.\n    |- Try 77 + 24 = 101. Add 101 to the number set. Current number set: [101, 4], target: 39, just two numbers left.\n     |- Try 101 + 4 = 105. Evaluate 105 != 39, drop this branch.\n     |- Try 101 - 4 = 97. Evaluate 97 != 39, drop this branch.\n     |- Try 101 * 4 = 404. Evaluate 404 != 39, drop this branch.\n     |- Try 101 \/ 4 = 25.2. 25.2 is a decimal, drop this branch.\n    |- Try 77 - 24 = 53. Add 53 to the number set. Current number set: [53, 4], target: 39, just two numbers left.\n     |- Try 53 + 4 = 57. Evaluate 57 != 39, drop this branch.\n     |- Try 53 - 4 = 49. Evaluate 49 != 39, drop this branch.\n     |- Try 53 * 4 = 212. Evaluate 212 != 39, drop this branch.\n     |- Try 53 \/ 4 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 77 * 24 = 1848. Add 1848 to the number set. Current number set: [1848, 4], target: 39, just two numbers left.\n     |- Try 1848 + 4 = 1852. Evaluate 1852 != 39, drop this branch.\n     |- Try 1848 - 4 = 1844. Evaluate 1844 != 39, drop this branch.\n     |- Try 1848 * 4 = 7392. 7392 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1848 \/ 4 = 462. Evaluate 462 != 39, drop this branch.\n    |- Try 77 \/ 24 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (77, 4) (numbers left: [24]). Try possible operations.\n    |- Try 77 + 4 = 81. Add 81 to the number set. Current number set: [81, 24], target: 39, just two numbers left.\n     |- Try 81 + 24 = 105. Evaluate 105 != 39, drop this branch.\n     |- Try 81 - 24 = 57. Evaluate 57 != 39, drop this branch.\n     |- Try 81 * 24 = 1944. Evaluate 1944 != 39, drop this branch.\n     |- Try 81 \/ 24 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 77 - 4 = 73. Add 73 to the number set. Current number set: [73, 24], target: 39, just two numbers left.\n     |- Try 73 + 24 = 97. Evaluate 97 != 39, drop this branch.\n     |- Try 73 - 24 = 49. Evaluate 49 != 39, drop this branch.\n     |- Try 73 * 24 = 1752. Evaluate 1752 != 39, drop this branch.\n     |- Try 73 \/ 24 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 77 * 4 = 308. Add 308 to the number set. Current number set: [308, 24], target: 39, just two numbers left.\n     |- Try 308 + 24 = 332. Evaluate 332 != 39, drop this branch.\n     |- Try 308 - 24 = 284. Evaluate 284 != 39, drop this branch.\n     |- Try 308 * 24 = 7392. 7392 exceeds the maximum intermediate result, drop this branch.\n     |- Try 308 \/ 24 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 77 \/ 4 = 19.2. 19.2 is a decimal, drop this branch.\n   |- Pick two numbers (24, 4) (numbers left: [77]). Try possible operations.\n    |- Try 24 + 4 = 28. Add 28 to the number set. Current number set: [28, 77], target: 39, just two numbers left.\n     |- Try 77 + 28 = 105. Evaluate 105 != 39, drop this branch.\n     |- Try 77 - 28 = 49. Evaluate 49 != 39, drop this branch.\n     |- Try 77 * 28 = 2156. 2156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 28 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 24 - 4 = 20. Add 20 to the number set. Current number set: [20, 77], target: 39, just two numbers left.\n     |- Try 77 + 20 = 97. Evaluate 97 != 39, drop this branch.\n     |- Try 77 - 20 = 57. Evaluate 57 != 39, drop this branch.\n     |- Try 77 * 20 = 1540. Evaluate 1540 != 39, drop this branch.\n     |- Try 77 \/ 20 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 24 * 4 = 96. Add 96 to the number set. Current number set: [96, 77], target: 39, just two numbers left.\n     |- Try 96 + 77 = 173. Evaluate 173 != 39, drop this branch.\n     |- Try 96 - 77 = 19. Evaluate 19 != 39, drop this branch.\n     |- Try 96 * 77 = 7392. 7392 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 77 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 24 \/ 4 = 6. Add 6 to the number set. Current number set: [6, 77], target: 39, just two numbers left.\n     |- Try 77 + 6 = 83. Evaluate 83 != 39, drop this branch.\n     |- Try 77 - 6 = 71. Evaluate 71 != 39, drop this branch.\n     |- Try 77 * 6 = 462. Evaluate 462 != 39, drop this branch.\n     |- Try 77 \/ 6 = 12.8. 12.8 is a decimal, drop this branch.\n  |- Try 44 - 33 = 11. Add 11 to the number set. Current number set: [11, 24, 4], target: 39. Options for choosing two numbers: [(11, 24), (11, 4), (24, 4)].\n   |- Pick two numbers (11, 24) (numbers left: [4]). Try possible operations.\n    |- Try 24 + 11 = 35. Add 35 to the number set. Current number set: [35, 4], target: 39, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 == 39, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 + 4 = 39\nThe step before: 24 + 11 = 35\nThe first step: 44 - 33 = 11\n\nOutput the solution in the required format:\n<Solution>\n44 - 33 = 11\n24 + 11 = 35\n35 + 4 = 39\n<\/Solution>\n","item":{"nums":[33,44,24,4],"solution":["44 - 33 = 11","24 + 11 = 35","35 + 4 = 39"],"target":39}}
+{"instance_id":"countdown_2k_99","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 45, 10, 32]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [8, 45, 10, 32], target: 15. Options for choosing two numbers: [(8, 45), (8, 10), (8, 32), (45, 10), (45, 32), (10, 32)].\n |- Pick two numbers (8, 45) (numbers left: [10, 32]). Try possible operations.\n  |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 10, 32], target: 15. Options for choosing two numbers: [(53, 10), (53, 32), (10, 32)].\n   |- Pick two numbers (53, 10) (numbers left: [32]). Try possible operations.\n    |- Try 53 + 10 = 63. Add 63 to the number set. Current number set: [63, 32], target: 15, just two numbers left.\n     |- Try 63 + 32 = 95. Evaluate 95 != 15, drop this branch.\n     |- Try 63 - 32 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 63 * 32 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 32 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 53 - 10 = 43. Add 43 to the number set. Current number set: [43, 32], target: 15, just two numbers left.\n     |- Try 43 + 32 = 75. Evaluate 75 != 15, drop this branch.\n     |- Try 43 - 32 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 43 * 32 = 1376. Evaluate 1376 != 15, drop this branch.\n     |- Try 43 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 53 * 10 = 530. Add 530 to the number set. Current number set: [530, 32], target: 15, just two numbers left.\n     |- Try 530 + 32 = 562. Evaluate 562 != 15, drop this branch.\n     |- Try 530 - 32 = 498. Evaluate 498 != 15, drop this branch.\n     |- Try 530 * 32 = 16960. 16960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 530 \/ 32 = 16.6. 16.6 is a decimal, drop this branch.\n    |- Try 53 \/ 10 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (53, 32) (numbers left: [10]). Try possible operations.\n    |- Try 53 + 32 = 85. Add 85 to the number set. Current number set: [85, 10], target: 15, just two numbers left.\n     |- Try 85 + 10 = 95. Evaluate 95 != 15, drop this branch.\n     |- Try 85 - 10 = 75. Evaluate 75 != 15, drop this branch.\n     |- Try 85 * 10 = 850. Evaluate 850 != 15, drop this branch.\n     |- Try 85 \/ 10 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 53 - 32 = 21. Add 21 to the number set. Current number set: [21, 10], target: 15, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 15, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 53 * 32 = 1696. Add 1696 to the number set. Current number set: [1696, 10], target: 15, just two numbers left.\n     |- Try 1696 + 10 = 1706. Evaluate 1706 != 15, drop this branch.\n     |- Try 1696 - 10 = 1686. Evaluate 1686 != 15, drop this branch.\n     |- Try 1696 * 10 = 16960. 16960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1696 \/ 10 = 169.6. 169.6 is a decimal, drop this branch.\n    |- Try 53 \/ 32 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 32) (numbers left: [53]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 53], target: 15, just two numbers left.\n     |- Try 53 + 42 = 95. Evaluate 95 != 15, drop this branch.\n     |- Try 53 - 42 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 53 * 42 = 2226. 2226 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 42 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 53], target: 15, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 15, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 15, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 32 * 10 = 320. Add 320 to the number set. Current number set: [320, 53], target: 15, just two numbers left.\n     |- Try 320 + 53 = 373. Evaluate 373 != 15, drop this branch.\n     |- Try 320 - 53 = 267. Evaluate 267 != 15, drop this branch.\n     |- Try 320 * 53 = 16960. 16960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 53 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 10, 32], target: 15. Options for choosing two numbers: [(37, 10), (37, 32), (10, 32)].\n   |- Pick two numbers (37, 10) (numbers left: [32]). Try possible operations.\n    |- Try 37 + 10 = 47. Add 47 to the number set. Current number set: [47, 32], target: 15, just two numbers left.\n     |- Try 47 + 32 = 79. Evaluate 79 != 15, drop this branch.\n     |- Try 47 - 32 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 - 32 = 15\nThe step before: 37 + 10 = 47\nThe first step: 45 - 8 = 37\n\nOutput the solution in the required format:\n<Solution>\n45 - 8 = 37\n37 + 10 = 47\n47 - 32 = 15\n<\/Solution>\n","item":{"nums":[8,45,10,32],"solution":["45 - 8 = 37","37 + 10 = 47","47 - 32 = 15"],"target":15}}
+{"instance_id":"countdown_2k_100","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 38, 22, 42]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [27, 38, 22, 42], target: 31. Options for choosing two numbers: [(27, 38), (27, 22), (27, 42), (38, 22), (38, 42), (22, 42)].\n |- Pick two numbers (27, 38) (numbers left: [22, 42]). Try possible operations.\n  |- Try 38 + 27 = 65. Add 65 to the number set. Current number set: [65, 22, 42], target: 31. Options for choosing two numbers: [(65, 22), (65, 42), (22, 42)].\n   |- Pick two numbers (65, 22) (numbers left: [42]). Try possible operations.\n    |- Try 65 + 22 = 87. Add 87 to the number set. Current number set: [87, 42], target: 31, just two numbers left.\n     |- Try 87 + 42 = 129. Evaluate 129 != 31, drop this branch.\n     |- Try 87 - 42 = 45. Evaluate 45 != 31, drop this branch.\n     |- Try 87 * 42 = 3654. 3654 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 42 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 65 - 22 = 43. Add 43 to the number set. Current number set: [43, 42], target: 31, just two numbers left.\n     |- Try 43 + 42 = 85. Evaluate 85 != 31, drop this branch.\n     |- Try 43 - 42 = 1. Evaluate 1 != 31, drop this branch.\n     |- Try 43 * 42 = 1806. Evaluate 1806 != 31, drop this branch.\n     |- Try 43 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 65 * 22 = 1430. Add 1430 to the number set. Current number set: [1430, 42], target: 31, just two numbers left.\n     |- Try 1430 + 42 = 1472. Evaluate 1472 != 31, drop this branch.\n     |- Try 1430 - 42 = 1388. Evaluate 1388 != 31, drop this branch.\n     |- Try 1430 * 42 = 60060. 60060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1430 \/ 42 = 34.0. 34.0 is a decimal, drop this branch.\n    |- Try 65 \/ 22 = 3.0. 3.0 is a decimal, drop this branch.\n   |- Pick two numbers (65, 42) (numbers left: [22]). Try possible operations.\n    |- Try 65 + 42 = 107. Add 107 to the number set. Current number set: [107, 22], target: 31, just two numbers left.\n     |- Try 107 + 22 = 129. Evaluate 129 != 31, drop this branch.\n     |- Try 107 - 22 = 85. Evaluate 85 != 31, drop this branch.\n     |- Try 107 * 22 = 2354. 2354 exceeds the maximum intermediate result, drop this branch.\n     |- Try 107 \/ 22 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 65 - 42 = 23. Add 23 to the number set. Current number set: [23, 22], target: 31, just two numbers left.\n     |- Try 23 + 22 = 45. Evaluate 45 != 31, drop this branch.\n     |- Try 23 - 22 = 1. Evaluate 1 != 31, drop this branch.\n     |- Try 23 * 22 = 506. Evaluate 506 != 31, drop this branch.\n     |- Try 23 \/ 22 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 65 * 42 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n    |- Try 65 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 42) (numbers left: [65]). Try possible operations.\n    |- Try 42 + 22 = 64. Add 64 to the number set. Current number set: [64, 65], target: 31, just two numbers left.\n     |- Try 65 + 64 = 129. Evaluate 129 != 31, drop this branch.\n     |- Try 65 - 64 = 1. Evaluate 1 != 31, drop this branch.\n     |- Try 65 * 64 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 64 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 42 - 22 = 20. Add 20 to the number set. Current number set: [20, 65], target: 31, just two numbers left.\n     |- Try 65 + 20 = 85. Evaluate 85 != 31, drop this branch.\n     |- Try 65 - 20 = 45. Evaluate 45 != 31, drop this branch.\n     |- Try 65 * 20 = 1300. Evaluate 1300 != 31, drop this branch.\n     |- Try 65 \/ 20 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 42 * 22 = 924. Add 924 to the number set. Current number set: [924, 65], target: 31, just two numbers left.\n     |- Try 924 + 65 = 989. Evaluate 989 != 31, drop this branch.\n     |- Try 924 - 65 = 859. Evaluate 859 != 31, drop this branch.\n     |- Try 924 * 65 = 60060. 60060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 65 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 42 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 38 - 27 = 11. Add 11 to the number set. Current number set: [11, 22, 42], target: 31. Options for choosing two numbers: [(11, 22), (11, 42), (22, 42)].\n   |- Pick two numbers (11, 22) (numbers left: [42]). Try possible operations.\n    |- Try 22 + 11 = 33. Add 33 to the number set. Current number set: [33, 42], target: 31, just two numbers left.\n     |- Try 42 + 33 = 75. Evaluate 75 != 31, drop this branch.\n     |- Try 42 - 33 = 9. Evaluate 9 != 31, drop this branch.\n     |- Try 42 * 33 = 1386. Evaluate 1386 != 31, drop this branch.\n     |- Try 42 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 22 - 11 = 11. Add 11 to the number set. Current number set: [11, 42], target: 31, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 31, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 42 - 11 = 31\nThe step before: 22 - 11 = 11\nThe first step: 38 - 27 = 11\n\nOutput the solution in the required format:\n<Solution>\n38 - 27 = 11\n22 - 11 = 11\n42 - 11 = 31\n<\/Solution>\n","item":{"nums":[27,38,22,42],"solution":["38 - 27 = 11","22 - 11 = 11","42 - 11 = 31"],"target":31}}
+{"instance_id":"countdown_2k_101","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 31, 45, 8]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [44, 31, 45, 8], target: 50. Options for choosing two numbers: [(44, 31), (44, 45), (44, 8), (31, 45), (31, 8), (45, 8)].\n |- Pick two numbers (44, 31) (numbers left: [45, 8]). Try possible operations.\n  |- Try 44 + 31 = 75. Add 75 to the number set. Current number set: [75, 45, 8], target: 50. Options for choosing two numbers: [(75, 45), (75, 8), (45, 8)].\n   |- Pick two numbers (75, 45) (numbers left: [8]). Try possible operations.\n    |- Try 75 + 45 = 120. Add 120 to the number set. Current number set: [120, 8], target: 50, just two numbers left.\n     |- Try 120 + 8 = 128. Evaluate 128 != 50, drop this branch.\n     |- Try 120 - 8 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 120 * 8 = 960. Evaluate 960 != 50, drop this branch.\n     |- Try 120 \/ 8 = 15. Evaluate 15 != 50, drop this branch.\n    |- Try 75 - 45 = 30. Add 30 to the number set. Current number set: [30, 8], target: 50, just two numbers left.\n     |- Try 30 + 8 = 38. Evaluate 38 != 50, drop this branch.\n     |- Try 30 - 8 = 22. Evaluate 22 != 50, drop this branch.\n     |- Try 30 * 8 = 240. Evaluate 240 != 50, drop this branch.\n     |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 75 * 45 = 3375. 3375 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 45 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (75, 8) (numbers left: [45]). Try possible operations.\n    |- Try 75 + 8 = 83. Add 83 to the number set. Current number set: [83, 45], target: 50, just two numbers left.\n     |- Try 83 + 45 = 128. Evaluate 128 != 50, drop this branch.\n     |- Try 83 - 45 = 38. Evaluate 38 != 50, drop this branch.\n     |- Try 83 * 45 = 3735. 3735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 75 - 8 = 67. Add 67 to the number set. Current number set: [67, 45], target: 50, just two numbers left.\n     |- Try 67 + 45 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 67 - 45 = 22. Evaluate 22 != 50, drop this branch.\n     |- Try 67 * 45 = 3015. 3015 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 45 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 75 * 8 = 600. Add 600 to the number set. Current number set: [600, 45], target: 50, just two numbers left.\n     |- Try 600 + 45 = 645. Evaluate 645 != 50, drop this branch.\n     |- Try 600 - 45 = 555. Evaluate 555 != 50, drop this branch.\n     |- Try 600 * 45 = 27000. 27000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 45 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 75 \/ 8 = 9.4. 9.4 is a decimal, drop this branch.\n   |- Pick two numbers (45, 8) (numbers left: [75]). Try possible operations.\n    |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 75], target: 50, just two numbers left.\n     |- Try 75 + 53 = 128. Evaluate 128 != 50, drop this branch.\n     |- Try 75 - 53 = 22. Evaluate 22 != 50, drop this branch.\n     |- Try 75 * 53 = 3975. 3975 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 53 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 75], target: 50, just two numbers left.\n     |- Try 75 + 37 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 75 - 37 = 38. Evaluate 38 != 50, drop this branch.\n     |- Try 75 * 37 = 2775. 2775 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 37 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 45 * 8 = 360. Add 360 to the number set. Current number set: [360, 75], target: 50, just two numbers left.\n     |- Try 360 + 75 = 435. Evaluate 435 != 50, drop this branch.\n     |- Try 360 - 75 = 285. Evaluate 285 != 50, drop this branch.\n     |- Try 360 * 75 = 27000. 27000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 75 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 44 - 31 = 13. Add 13 to the number set. Current number set: [13, 45, 8], target: 50. Options for choosing two numbers: [(13, 45), (13, 8), (45, 8)].\n   |- Pick two numbers (13, 45) (numbers left: [8]). Try possible operations.\n    |- Try 45 + 13 = 58. Add 58 to the number set. Current number set: [58, 8], target: 50, just two numbers left.\n     |- Try 58 + 8 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 58 - 8 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 58 - 8 = 50\nThe step before: 45 + 13 = 58\nThe first step: 44 - 31 = 13\n\nOutput the solution in the required format:\n<Solution>\n44 - 31 = 13\n45 + 13 = 58\n58 - 8 = 50\n<\/Solution>\n","item":{"nums":[44,31,45,8],"solution":["44 - 31 = 13","45 + 13 = 58","58 - 8 = 50"],"target":50}}
+{"instance_id":"countdown_2k_102","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 34, 19, 24]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [9, 34, 19, 24], target: 20. Options for choosing two numbers: [(9, 34), (9, 19), (9, 24), (34, 19), (34, 24), (19, 24)].\n |- Pick two numbers (9, 34) (numbers left: [19, 24]). Try possible operations.\n  |- Try 34 + 9 = 43. Add 43 to the number set. Current number set: [43, 19, 24], target: 20. Options for choosing two numbers: [(43, 19), (43, 24), (19, 24)].\n   |- Pick two numbers (43, 19) (numbers left: [24]). Try possible operations.\n    |- Try 43 + 19 = 62. Add 62 to the number set. Current number set: [62, 24], target: 20, just two numbers left.\n     |- Try 62 + 24 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 62 - 24 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 62 * 24 = 1488. Evaluate 1488 != 20, drop this branch.\n     |- Try 62 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 43 - 19 = 24. Add 24 to the number set. Current number set: [24, 24], target: 20, just two numbers left.\n     |- Try 24 + 24 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 24 - 24 = 0. Evaluate 0 != 20, drop this branch.\n     |- Try 24 * 24 = 576. Evaluate 576 != 20, drop this branch.\n     |- Try 24 \/ 24 = 1. Evaluate 1 != 20, drop this branch.\n    |- Try 43 * 19 = 817. Add 817 to the number set. Current number set: [817, 24], target: 20, just two numbers left.\n     |- Try 817 + 24 = 841. Evaluate 841 != 20, drop this branch.\n     |- Try 817 - 24 = 793. Evaluate 793 != 20, drop this branch.\n     |- Try 817 * 24 = 19608. 19608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 817 \/ 24 = 34.0. 34.0 is a decimal, drop this branch.\n    |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (43, 24) (numbers left: [19]). Try possible operations.\n    |- Try 43 + 24 = 67. Add 67 to the number set. Current number set: [67, 19], target: 20, just two numbers left.\n     |- Try 67 + 19 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 67 - 19 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 67 * 19 = 1273. Evaluate 1273 != 20, drop this branch.\n     |- Try 67 \/ 19 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 43 - 24 = 19. Add 19 to the number set. Current number set: [19, 19], target: 20, just two numbers left.\n     |- Try 19 + 19 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 19 - 19 = 0. Evaluate 0 != 20, drop this branch.\n     |- Try 19 * 19 = 361. Evaluate 361 != 20, drop this branch.\n     |- Try 19 \/ 19 = 1. Evaluate 1 != 20, drop this branch.\n    |- Try 43 * 24 = 1032. Add 1032 to the number set. Current number set: [1032, 19], target: 20, just two numbers left.\n     |- Try 1032 + 19 = 1051. Evaluate 1051 != 20, drop this branch.\n     |- Try 1032 - 19 = 1013. Evaluate 1013 != 20, drop this branch.\n     |- Try 1032 * 19 = 19608. 19608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1032 \/ 19 = 54.3. 54.3 is a decimal, drop this branch.\n    |- Try 43 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (19, 24) (numbers left: [43]). Try possible operations.\n    |- Try 24 + 19 = 43. Add 43 to the number set. Current number set: [43, 43], target: 20, just two numbers left.\n     |- Try 43 + 43 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 43 - 43 = 0. Evaluate 0 != 20, drop this branch.\n     |- Try 43 * 43 = 1849. Evaluate 1849 != 20, drop this branch.\n     |- Try 43 \/ 43 = 1. Evaluate 1 != 20, drop this branch.\n    |- Try 24 - 19 = 5. Add 5 to the number set. Current number set: [5, 43], target: 20, just two numbers left.\n     |- Try 43 + 5 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 43 - 5 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 43 * 5 = 215. Evaluate 215 != 20, drop this branch.\n     |- Try 43 \/ 5 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 24 * 19 = 456. Add 456 to the number set. Current number set: [456, 43], target: 20, just two numbers left.\n     |- Try 456 + 43 = 499. Evaluate 499 != 20, drop this branch.\n     |- Try 456 - 43 = 413. Evaluate 413 != 20, drop this branch.\n     |- Try 456 * 43 = 19608. 19608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 456 \/ 43 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 34 - 9 = 25. Add 25 to the number set. Current number set: [25, 19, 24], target: 20. Options for choosing two numbers: [(25, 19), (25, 24), (19, 24)].\n   |- Pick two numbers (25, 19) (numbers left: [24]). Try possible operations.\n    |- Try 25 + 19 = 44. Add 44 to the number set. Current number set: [44, 24], target: 20, just two numbers left.\n     |- Try 44 + 24 = 68. Evaluate 68 != 20, drop this branch.\n     |- Try 44 - 24 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 24 = 20\nThe step before: 25 + 19 = 44\nThe first step: 34 - 9 = 25\n\nOutput the solution in the required format:\n<Solution>\n34 - 9 = 25\n25 + 19 = 44\n44 - 24 = 20\n<\/Solution>\n","item":{"nums":[9,34,19,24],"solution":["34 - 9 = 25","25 + 19 = 44","44 - 24 = 20"],"target":20}}
+{"instance_id":"countdown_2k_103","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 40, 16, 33]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [47, 40, 16, 33], target: 42. Options for choosing two numbers: [(47, 40), (47, 16), (47, 33), (40, 16), (40, 33), (16, 33)].\n |- Pick two numbers (47, 40) (numbers left: [16, 33]). Try possible operations.\n  |- Try 47 + 40 = 87. Add 87 to the number set. Current number set: [87, 16, 33], target: 42. Options for choosing two numbers: [(87, 16), (87, 33), (16, 33)].\n   |- Pick two numbers (87, 16) (numbers left: [33]). Try possible operations.\n    |- Try 87 + 16 = 103. Add 103 to the number set. Current number set: [103, 33], target: 42, just two numbers left.\n     |- Try 103 + 33 = 136. Evaluate 136 != 42, drop this branch.\n     |- Try 103 - 33 = 70. Evaluate 70 != 42, drop this branch.\n     |- Try 103 * 33 = 3399. 3399 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 33 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 87 - 16 = 71. Add 71 to the number set. Current number set: [71, 33], target: 42, just two numbers left.\n     |- Try 71 + 33 = 104. Evaluate 104 != 42, drop this branch.\n     |- Try 71 - 33 = 38. Evaluate 38 != 42, drop this branch.\n     |- Try 71 * 33 = 2343. 2343 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 87 * 16 = 1392. Add 1392 to the number set. Current number set: [1392, 33], target: 42, just two numbers left.\n     |- Try 1392 + 33 = 1425. Evaluate 1425 != 42, drop this branch.\n     |- Try 1392 - 33 = 1359. Evaluate 1359 != 42, drop this branch.\n     |- Try 1392 * 33 = 45936. 45936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1392 \/ 33 = 42.2. 42.2 is a decimal, drop this branch.\n    |- Try 87 \/ 16 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (87, 33) (numbers left: [16]). Try possible operations.\n    |- Try 87 + 33 = 120. Add 120 to the number set. Current number set: [120, 16], target: 42, just two numbers left.\n     |- Try 120 + 16 = 136. Evaluate 136 != 42, drop this branch.\n     |- Try 120 - 16 = 104. Evaluate 104 != 42, drop this branch.\n     |- Try 120 * 16 = 1920. Evaluate 1920 != 42, drop this branch.\n     |- Try 120 \/ 16 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 87 - 33 = 54. Add 54 to the number set. Current number set: [54, 16], target: 42, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 42, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 42, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 42, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 87 * 33 = 2871. 2871 exceeds the maximum intermediate result, drop this branch.\n    |- Try 87 \/ 33 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (16, 33) (numbers left: [87]). Try possible operations.\n    |- Try 33 + 16 = 49. Add 49 to the number set. Current number set: [49, 87], target: 42, just two numbers left.\n     |- Try 87 + 49 = 136. Evaluate 136 != 42, drop this branch.\n     |- Try 87 - 49 = 38. Evaluate 38 != 42, drop this branch.\n     |- Try 87 * 49 = 4263. 4263 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 49 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 33 - 16 = 17. Add 17 to the number set. Current number set: [17, 87], target: 42, just two numbers left.\n     |- Try 87 + 17 = 104. Evaluate 104 != 42, drop this branch.\n     |- Try 87 - 17 = 70. Evaluate 70 != 42, drop this branch.\n     |- Try 87 * 17 = 1479. Evaluate 1479 != 42, drop this branch.\n     |- Try 87 \/ 17 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 33 * 16 = 528. Add 528 to the number set. Current number set: [528, 87], target: 42, just two numbers left.\n     |- Try 528 + 87 = 615. Evaluate 615 != 42, drop this branch.\n     |- Try 528 - 87 = 441. Evaluate 441 != 42, drop this branch.\n     |- Try 528 * 87 = 45936. 45936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 87 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 33 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 47 - 40 = 7. Add 7 to the number set. Current number set: [7, 16, 33], target: 42. Options for choosing two numbers: [(7, 16), (7, 33), (16, 33)].\n   |- Pick two numbers (7, 16) (numbers left: [33]). Try possible operations.\n    |- Try 16 + 7 = 23. Add 23 to the number set. Current number set: [23, 33], target: 42, just two numbers left.\n     |- Try 33 + 23 = 56. Evaluate 56 != 42, drop this branch.\n     |- Try 33 - 23 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 33 * 23 = 759. Evaluate 759 != 42, drop this branch.\n     |- Try 33 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 16 - 7 = 9. Add 9 to the number set. Current number set: [9, 33], target: 42, just two numbers left.\n     |- Try 33 + 9 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 + 9 = 42\nThe step before: 16 - 7 = 9\nThe first step: 47 - 40 = 7\n\nOutput the solution in the required format:\n<Solution>\n47 - 40 = 7\n16 - 7 = 9\n33 + 9 = 42\n<\/Solution>\n","item":{"nums":[47,40,16,33],"solution":["47 - 40 = 7","16 - 7 = 9","33 + 9 = 42"],"target":42}}
+{"instance_id":"countdown_2k_104","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [45, 38, 12, 29]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [45, 38, 12, 29], target: 10. Options for choosing two numbers: [(45, 38), (45, 12), (45, 29), (38, 12), (38, 29), (12, 29)].\n |- Pick two numbers (45, 38) (numbers left: [12, 29]). Try possible operations.\n  |- Try 45 + 38 = 83. Add 83 to the number set. Current number set: [83, 12, 29], target: 10. Options for choosing two numbers: [(83, 12), (83, 29), (12, 29)].\n   |- Pick two numbers (83, 12) (numbers left: [29]). Try possible operations.\n    |- Try 83 + 12 = 95. Add 95 to the number set. Current number set: [95, 29], target: 10, just two numbers left.\n     |- Try 95 + 29 = 124. Evaluate 124 != 10, drop this branch.\n     |- Try 95 - 29 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 95 * 29 = 2755. 2755 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 29 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 83 - 12 = 71. Add 71 to the number set. Current number set: [71, 29], target: 10, just two numbers left.\n     |- Try 71 + 29 = 100. Evaluate 100 != 10, drop this branch.\n     |- Try 71 - 29 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 71 * 29 = 2059. 2059 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 29 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 83 * 12 = 996. Add 996 to the number set. Current number set: [996, 29], target: 10, just two numbers left.\n     |- Try 996 + 29 = 1025. Evaluate 1025 != 10, drop this branch.\n     |- Try 996 - 29 = 967. Evaluate 967 != 10, drop this branch.\n     |- Try 996 * 29 = 28884. 28884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 996 \/ 29 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 83 \/ 12 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (83, 29) (numbers left: [12]). Try possible operations.\n    |- Try 83 + 29 = 112. Add 112 to the number set. Current number set: [112, 12], target: 10, just two numbers left.\n     |- Try 112 + 12 = 124. Evaluate 124 != 10, drop this branch.\n     |- Try 112 - 12 = 100. Evaluate 100 != 10, drop this branch.\n     |- Try 112 * 12 = 1344. Evaluate 1344 != 10, drop this branch.\n     |- Try 112 \/ 12 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 83 - 29 = 54. Add 54 to the number set. Current number set: [54, 12], target: 10, just two numbers left.\n     |- Try 54 + 12 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 54 - 12 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 54 * 12 = 648. Evaluate 648 != 10, drop this branch.\n     |- Try 54 \/ 12 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 83 * 29 = 2407. 2407 exceeds the maximum intermediate result, drop this branch.\n    |- Try 83 \/ 29 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (12, 29) (numbers left: [83]). Try possible operations.\n    |- Try 29 + 12 = 41. Add 41 to the number set. Current number set: [41, 83], target: 10, just two numbers left.\n     |- Try 83 + 41 = 124. Evaluate 124 != 10, drop this branch.\n     |- Try 83 - 41 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 83 * 41 = 3403. 3403 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 29 - 12 = 17. Add 17 to the number set. Current number set: [17, 83], target: 10, just two numbers left.\n     |- Try 83 + 17 = 100. Evaluate 100 != 10, drop this branch.\n     |- Try 83 - 17 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 83 * 17 = 1411. Evaluate 1411 != 10, drop this branch.\n     |- Try 83 \/ 17 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 29 * 12 = 348. Add 348 to the number set. Current number set: [348, 83], target: 10, just two numbers left.\n     |- Try 348 + 83 = 431. Evaluate 431 != 10, drop this branch.\n     |- Try 348 - 83 = 265. Evaluate 265 != 10, drop this branch.\n     |- Try 348 * 83 = 28884. 28884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 348 \/ 83 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 29 \/ 12 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 45 - 38 = 7. Add 7 to the number set. Current number set: [7, 12, 29], target: 10. Options for choosing two numbers: [(7, 12), (7, 29), (12, 29)].\n   |- Pick two numbers (7, 12) (numbers left: [29]). Try possible operations.\n    |- Try 12 + 7 = 19. Add 19 to the number set. Current number set: [19, 29], target: 10, just two numbers left.\n     |- Try 29 + 19 = 48. Evaluate 48 != 10, drop this branch.\n     |- Try 29 - 19 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 - 19 = 10\nThe step before: 12 + 7 = 19\nThe first step: 45 - 38 = 7\n\nOutput the solution in the required format:\n<Solution>\n45 - 38 = 7\n12 + 7 = 19\n29 - 19 = 10\n<\/Solution>\n","item":{"nums":[45,38,12,29],"solution":["45 - 38 = 7","12 + 7 = 19","29 - 19 = 10"],"target":10}}
+{"instance_id":"countdown_2k_105","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [25, 29, 30, 3]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [25, 29, 30, 3], target: 44. Options for choosing two numbers: [(25, 29), (25, 30), (25, 3), (29, 30), (29, 3), (30, 3)].\n |- Pick two numbers (25, 29) (numbers left: [30, 3]). Try possible operations.\n  |- Try 29 + 25 = 54. Add 54 to the number set. Current number set: [54, 30, 3], target: 44. Options for choosing two numbers: [(54, 30), (54, 3), (30, 3)].\n   |- Pick two numbers (54, 30) (numbers left: [3]). Try possible operations.\n    |- Try 54 + 30 = 84. Add 84 to the number set. Current number set: [84, 3], target: 44, just two numbers left.\n     |- Try 84 + 3 = 87. Evaluate 87 != 44, drop this branch.\n     |- Try 84 - 3 = 81. Evaluate 81 != 44, drop this branch.\n     |- Try 84 * 3 = 252. Evaluate 252 != 44, drop this branch.\n     |- Try 84 \/ 3 = 28. Evaluate 28 != 44, drop this branch.\n    |- Try 54 - 30 = 24. Add 24 to the number set. Current number set: [24, 3], target: 44, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 44, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 != 44, drop this branch.\n     |- Try 24 * 3 = 72. Evaluate 72 != 44, drop this branch.\n     |- Try 24 \/ 3 = 8. Evaluate 8 != 44, drop this branch.\n    |- Try 54 * 30 = 1620. Add 1620 to the number set. Current number set: [1620, 3], target: 44, just two numbers left.\n     |- Try 1620 + 3 = 1623. Evaluate 1623 != 44, drop this branch.\n     |- Try 1620 - 3 = 1617. Evaluate 1617 != 44, drop this branch.\n     |- Try 1620 * 3 = 4860. 4860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1620 \/ 3 = 540. Evaluate 540 != 44, drop this branch.\n    |- Try 54 \/ 30 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (54, 3) (numbers left: [30]). Try possible operations.\n    |- Try 54 + 3 = 57. Add 57 to the number set. Current number set: [57, 30], target: 44, just two numbers left.\n     |- Try 57 + 30 = 87. Evaluate 87 != 44, drop this branch.\n     |- Try 57 - 30 = 27. Evaluate 27 != 44, drop this branch.\n     |- Try 57 * 30 = 1710. Evaluate 1710 != 44, drop this branch.\n     |- Try 57 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 54 - 3 = 51. Add 51 to the number set. Current number set: [51, 30], target: 44, just two numbers left.\n     |- Try 51 + 30 = 81. Evaluate 81 != 44, drop this branch.\n     |- Try 51 - 30 = 21. Evaluate 21 != 44, drop this branch.\n     |- Try 51 * 30 = 1530. Evaluate 1530 != 44, drop this branch.\n     |- Try 51 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 54 * 3 = 162. Add 162 to the number set. Current number set: [162, 30], target: 44, just two numbers left.\n     |- Try 162 + 30 = 192. Evaluate 192 != 44, drop this branch.\n     |- Try 162 - 30 = 132. Evaluate 132 != 44, drop this branch.\n     |- Try 162 * 30 = 4860. 4860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 30 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 54 \/ 3 = 18. Add 18 to the number set. Current number set: [18, 30], target: 44, just two numbers left.\n     |- Try 30 + 18 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 30 - 18 = 12. Evaluate 12 != 44, drop this branch.\n     |- Try 30 * 18 = 540. Evaluate 540 != 44, drop this branch.\n     |- Try 30 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (30, 3) (numbers left: [54]). Try possible operations.\n    |- Try 30 + 3 = 33. Add 33 to the number set. Current number set: [33, 54], target: 44, just two numbers left.\n     |- Try 54 + 33 = 87. Evaluate 87 != 44, drop this branch.\n     |- Try 54 - 33 = 21. Evaluate 21 != 44, drop this branch.\n     |- Try 54 * 33 = 1782. Evaluate 1782 != 44, drop this branch.\n     |- Try 54 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 30 - 3 = 27. Add 27 to the number set. Current number set: [27, 54], target: 44, just two numbers left.\n     |- Try 54 + 27 = 81. Evaluate 81 != 44, drop this branch.\n     |- Try 54 - 27 = 27. Evaluate 27 != 44, drop this branch.\n     |- Try 54 * 27 = 1458. Evaluate 1458 != 44, drop this branch.\n     |- Try 54 \/ 27 = 2. Evaluate 2 != 44, drop this branch.\n    |- Try 30 * 3 = 90. Add 90 to the number set. Current number set: [90, 54], target: 44, just two numbers left.\n     |- Try 90 + 54 = 144. Evaluate 144 != 44, drop this branch.\n     |- Try 90 - 54 = 36. Evaluate 36 != 44, drop this branch.\n     |- Try 90 * 54 = 4860. 4860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 54 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 30 \/ 3 = 10. Add 10 to the number set. Current number set: [10, 54], target: 44, just two numbers left.\n     |- Try 54 + 10 = 64. Evaluate 64 != 44, drop this branch.\n     |- Try 54 - 10 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 54 - 10 = 44\nThe step before: 30 \/ 3 = 10\nThe first step: 29 + 25 = 54\n\nOutput the solution in the required format:\n<Solution>\n29 + 25 = 54\n30 \/ 3 = 10\n54 - 10 = 44\n<\/Solution>\n","item":{"nums":[25,29,30,3],"solution":["29 + 25 = 54","30 \/ 3 = 10","54 - 10 = 44"],"target":44}}
+{"instance_id":"countdown_2k_106","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 49, 8, 37]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [32, 49, 8, 37], target: 12. Options for choosing two numbers: [(32, 49), (32, 8), (32, 37), (49, 8), (49, 37), (8, 37)].\n |- Pick two numbers (32, 49) (numbers left: [8, 37]). Try possible operations.\n  |- Try 49 + 32 = 81. Add 81 to the number set. Current number set: [81, 8, 37], target: 12. Options for choosing two numbers: [(81, 8), (81, 37), (8, 37)].\n   |- Pick two numbers (81, 8) (numbers left: [37]). Try possible operations.\n    |- Try 81 + 8 = 89. Add 89 to the number set. Current number set: [89, 37], target: 12, just two numbers left.\n     |- Try 89 + 37 = 126. Evaluate 126 != 12, drop this branch.\n     |- Try 89 - 37 = 52. Evaluate 52 != 12, drop this branch.\n     |- Try 89 * 37 = 3293. 3293 exceeds the maximum intermediate result, drop this branch.\n     |- Try 89 \/ 37 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 81 - 8 = 73. Add 73 to the number set. Current number set: [73, 37], target: 12, just two numbers left.\n     |- Try 73 + 37 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 73 - 37 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 73 * 37 = 2701. 2701 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 37 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 81 * 8 = 648. Add 648 to the number set. Current number set: [648, 37], target: 12, just two numbers left.\n     |- Try 648 + 37 = 685. Evaluate 685 != 12, drop this branch.\n     |- Try 648 - 37 = 611. Evaluate 611 != 12, drop this branch.\n     |- Try 648 * 37 = 23976. 23976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 37 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 81 \/ 8 = 10.1. 10.1 is a decimal, drop this branch.\n   |- Pick two numbers (81, 37) (numbers left: [8]). Try possible operations.\n    |- Try 81 + 37 = 118. Add 118 to the number set. Current number set: [118, 8], target: 12, just two numbers left.\n     |- Try 118 + 8 = 126. Evaluate 126 != 12, drop this branch.\n     |- Try 118 - 8 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 118 * 8 = 944. Evaluate 944 != 12, drop this branch.\n     |- Try 118 \/ 8 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 81 - 37 = 44. Add 44 to the number set. Current number set: [44, 8], target: 12, just two numbers left.\n     |- Try 44 + 8 = 52. Evaluate 52 != 12, drop this branch.\n     |- Try 44 - 8 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 44 * 8 = 352. Evaluate 352 != 12, drop this branch.\n     |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 81 * 37 = 2997. 2997 exceeds the maximum intermediate result, drop this branch.\n    |- Try 81 \/ 37 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 37) (numbers left: [81]). Try possible operations.\n    |- Try 37 + 8 = 45. Add 45 to the number set. Current number set: [45, 81], target: 12, just two numbers left.\n     |- Try 81 + 45 = 126. Evaluate 126 != 12, drop this branch.\n     |- Try 81 - 45 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 81 * 45 = 3645. 3645 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 37 - 8 = 29. Add 29 to the number set. Current number set: [29, 81], target: 12, just two numbers left.\n     |- Try 81 + 29 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 81 - 29 = 52. Evaluate 52 != 12, drop this branch.\n     |- Try 81 * 29 = 2349. 2349 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 29 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 37 * 8 = 296. Add 296 to the number set. Current number set: [296, 81], target: 12, just two numbers left.\n     |- Try 296 + 81 = 377. Evaluate 377 != 12, drop this branch.\n     |- Try 296 - 81 = 215. Evaluate 215 != 12, drop this branch.\n     |- Try 296 * 81 = 23976. 23976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 296 \/ 81 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 37 \/ 8 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 49 - 32 = 17. Add 17 to the number set. Current number set: [17, 8, 37], target: 12. Options for choosing two numbers: [(17, 8), (17, 37), (8, 37)].\n   |- Pick two numbers (17, 8) (numbers left: [37]). Try possible operations.\n    |- Try 17 + 8 = 25. Add 25 to the number set. Current number set: [25, 37], target: 12, just two numbers left.\n     |- Try 37 + 25 = 62. Evaluate 62 != 12, drop this branch.\n     |- Try 37 - 25 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 37 - 25 = 12\nThe step before: 17 + 8 = 25\nThe first step: 49 - 32 = 17\n\nOutput the solution in the required format:\n<Solution>\n49 - 32 = 17\n17 + 8 = 25\n37 - 25 = 12\n<\/Solution>\n","item":{"nums":[32,49,8,37],"solution":["49 - 32 = 17","17 + 8 = 25","37 - 25 = 12"],"target":12}}
+{"instance_id":"countdown_2k_107","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 9, 24, 23]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [3, 9, 24, 23], target: 41. Options for choosing two numbers: [(3, 9), (3, 24), (3, 23), (9, 24), (9, 23), (24, 23)].\n |- Pick two numbers (3, 9) (numbers left: [24, 23]). Try possible operations.\n  |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 24, 23], target: 41. Options for choosing two numbers: [(12, 24), (12, 23), (24, 23)].\n   |- Pick two numbers (12, 24) (numbers left: [23]). Try possible operations.\n    |- Try 24 + 12 = 36. Add 36 to the number set. Current number set: [36, 23], target: 41, just two numbers left.\n     |- Try 36 + 23 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 36 - 23 = 13. Evaluate 13 != 41, drop this branch.\n     |- Try 36 * 23 = 828. Evaluate 828 != 41, drop this branch.\n     |- Try 36 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 24 - 12 = 12. Add 12 to the number set. Current number set: [12, 23], target: 41, just two numbers left.\n     |- Try 23 + 12 = 35. Evaluate 35 != 41, drop this branch.\n     |- Try 23 - 12 = 11. Evaluate 11 != 41, drop this branch.\n     |- Try 23 * 12 = 276. Evaluate 276 != 41, drop this branch.\n     |- Try 23 \/ 12 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 24 * 12 = 288. Add 288 to the number set. Current number set: [288, 23], target: 41, just two numbers left.\n     |- Try 288 + 23 = 311. Evaluate 311 != 41, drop this branch.\n     |- Try 288 - 23 = 265. Evaluate 265 != 41, drop this branch.\n     |- Try 288 * 23 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 23 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 24 \/ 12 = 2. Add 2 to the number set. Current number set: [2, 23], target: 41, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 != 41, drop this branch.\n     |- Try 23 - 2 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 23 * 2 = 46. Evaluate 46 != 41, drop this branch.\n     |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (12, 23) (numbers left: [24]). Try possible operations.\n    |- Try 23 + 12 = 35. Add 35 to the number set. Current number set: [35, 24], target: 41, just two numbers left.\n     |- Try 35 + 24 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 35 - 24 = 11. Evaluate 11 != 41, drop this branch.\n     |- Try 35 * 24 = 840. Evaluate 840 != 41, drop this branch.\n     |- Try 35 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 23 - 12 = 11. Add 11 to the number set. Current number set: [11, 24], target: 41, just two numbers left.\n     |- Try 24 + 11 = 35. Evaluate 35 != 41, drop this branch.\n     |- Try 24 - 11 = 13. Evaluate 13 != 41, drop this branch.\n     |- Try 24 * 11 = 264. Evaluate 264 != 41, drop this branch.\n     |- Try 24 \/ 11 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 23 * 12 = 276. Add 276 to the number set. Current number set: [276, 24], target: 41, just two numbers left.\n     |- Try 276 + 24 = 300. Evaluate 300 != 41, drop this branch.\n     |- Try 276 - 24 = 252. Evaluate 252 != 41, drop this branch.\n     |- Try 276 * 24 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 276 \/ 24 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 23 \/ 12 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (24, 23) (numbers left: [12]). Try possible operations.\n    |- Try 24 + 23 = 47. Add 47 to the number set. Current number set: [47, 12], target: 41, just two numbers left.\n     |- Try 47 + 12 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 47 - 12 = 35. Evaluate 35 != 41, drop this branch.\n     |- Try 47 * 12 = 564. Evaluate 564 != 41, drop this branch.\n     |- Try 47 \/ 12 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 24 - 23 = 1. Add 1 to the number set. Current number set: [1, 12], target: 41, just two numbers left.\n     |- Try 12 + 1 = 13. Evaluate 13 != 41, drop this branch.\n     |- Try 12 - 1 = 11. Evaluate 11 != 41, drop this branch.\n     |- Try 12 * 1 = 12. Evaluate 12 != 41, drop this branch.\n     |- Try 12 \/ 1 = 12. Evaluate 12 != 41, drop this branch.\n    |- Try 24 * 23 = 552. Add 552 to the number set. Current number set: [552, 12], target: 41, just two numbers left.\n     |- Try 552 + 12 = 564. Evaluate 564 != 41, drop this branch.\n     |- Try 552 - 12 = 540. Evaluate 540 != 41, drop this branch.\n     |- Try 552 * 12 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 552 \/ 12 = 46. Evaluate 46 != 41, drop this branch.\n    |- Try 24 \/ 23 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 24, 23], target: 41. Options for choosing two numbers: [(6, 24), (6, 23), (24, 23)].\n   |- Pick two numbers (6, 24) (numbers left: [23]). Try possible operations.\n    |- Try 24 + 6 = 30. Add 30 to the number set. Current number set: [30, 23], target: 41, just two numbers left.\n     |- Try 30 + 23 = 53. Evaluate 53 != 41, drop this branch.\n     |- Try 30 - 23 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 30 * 23 = 690. Evaluate 690 != 41, drop this branch.\n     |- Try 30 \/ 23 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 24 - 6 = 18. Add 18 to the number set. Current number set: [18, 23], target: 41, just two numbers left.\n     |- Try 23 + 18 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 18 = 41\nThe step before: 24 - 6 = 18\nThe first step: 9 - 3 = 6\n\nOutput the solution in the required format:\n<Solution>\n9 - 3 = 6\n24 - 6 = 18\n23 + 18 = 41\n<\/Solution>\n","item":{"nums":[3,9,24,23],"solution":["9 - 3 = 6","24 - 6 = 18","23 + 18 = 41"],"target":41}}
+{"instance_id":"countdown_2k_108","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [28, 13, 32, 41]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [28, 13, 32, 41], target: 31. Options for choosing two numbers: [(28, 13), (28, 32), (28, 41), (13, 32), (13, 41), (32, 41)].\n |- Pick two numbers (28, 13) (numbers left: [32, 41]). Try possible operations.\n  |- Try 28 + 13 = 41. Add 41 to the number set. Current number set: [41, 32, 41], target: 31. Options for choosing two numbers: [(41, 32), (41, 41), (32, 41)].\n   |- Pick two numbers (41, 32) (numbers left: [41]). Try possible operations.\n    |- Try 41 + 32 = 73. Add 73 to the number set. Current number set: [73, 41], target: 31, just two numbers left.\n     |- Try 73 + 41 = 114. Evaluate 114 != 31, drop this branch.\n     |- Try 73 - 41 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 73 * 41 = 2993. 2993 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 41 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 41 - 32 = 9. Add 9 to the number set. Current number set: [9, 41], target: 31, just two numbers left.\n     |- Try 41 + 9 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 41 - 9 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 41 * 9 = 369. Evaluate 369 != 31, drop this branch.\n     |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 41 * 32 = 1312. Add 1312 to the number set. Current number set: [1312, 41], target: 31, just two numbers left.\n     |- Try 1312 + 41 = 1353. Evaluate 1353 != 31, drop this branch.\n     |- Try 1312 - 41 = 1271. Evaluate 1271 != 31, drop this branch.\n     |- Try 1312 * 41 = 53792. 53792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1312 \/ 41 = 32. Evaluate 32 != 31, drop this branch.\n    |- Try 41 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (41, 41) (numbers left: [32]). Try possible operations.\n    |- Try 41 + 41 = 82. Add 82 to the number set. Current number set: [82, 32], target: 31, just two numbers left.\n     |- Try 82 + 32 = 114. Evaluate 114 != 31, drop this branch.\n     |- Try 82 - 32 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 82 * 32 = 2624. 2624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 32 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 41 - 41 = 0. Add 0 to the number set. Current number set: [0, 32], target: 31, just two numbers left.\n     |- Try 32 + 0 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 32 - 0 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 32 * 0 = 0. Evaluate 0 != 31, drop this branch.\n     |- Try 32 \/ 0 (invalid operation). drop this branch.\n    |- Try 41 * 41 = 1681. Add 1681 to the number set. Current number set: [1681, 32], target: 31, just two numbers left.\n     |- Try 1681 + 32 = 1713. Evaluate 1713 != 31, drop this branch.\n     |- Try 1681 - 32 = 1649. Evaluate 1649 != 31, drop this branch.\n     |- Try 1681 * 32 = 53792. 53792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1681 \/ 32 = 52.5. 52.5 is a decimal, drop this branch.\n    |- Try 41 \/ 41 = 1. Add 1 to the number set. Current number set: [1, 32], target: 31, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 31, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 - 1 = 31\nThe step before: 41 \/ 41 = 1\nThe first step: 28 + 13 = 41\n\nOutput the solution in the required format:\n<Solution>\n28 + 13 = 41\n41 \/ 41 = 1\n32 - 1 = 31\n<\/Solution>\n","item":{"nums":[28,13,32,41],"solution":["28 + 13 = 41","41 \/ 41 = 1","32 - 1 = 31"],"target":31}}
+{"instance_id":"countdown_2k_109","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [43, 49, 36, 12]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [43, 49, 36, 12], target: 42. Options for choosing two numbers: [(43, 49), (43, 36), (43, 12), (49, 36), (49, 12), (36, 12)].\n |- Pick two numbers (43, 49) (numbers left: [36, 12]). Try possible operations.\n  |- Try 49 + 43 = 92. Add 92 to the number set. Current number set: [92, 36, 12], target: 42. Options for choosing two numbers: [(92, 36), (92, 12), (36, 12)].\n   |- Pick two numbers (92, 36) (numbers left: [12]). Try possible operations.\n    |- Try 92 + 36 = 128. Add 128 to the number set. Current number set: [128, 12], target: 42, just two numbers left.\n     |- Try 128 + 12 = 140. Evaluate 140 != 42, drop this branch.\n     |- Try 128 - 12 = 116. Evaluate 116 != 42, drop this branch.\n     |- Try 128 * 12 = 1536. Evaluate 1536 != 42, drop this branch.\n     |- Try 128 \/ 12 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 92 - 36 = 56. Add 56 to the number set. Current number set: [56, 12], target: 42, just two numbers left.\n     |- Try 56 + 12 = 68. Evaluate 68 != 42, drop this branch.\n     |- Try 56 - 12 = 44. Evaluate 44 != 42, drop this branch.\n     |- Try 56 * 12 = 672. Evaluate 672 != 42, drop this branch.\n     |- Try 56 \/ 12 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 92 * 36 = 3312. 3312 exceeds the maximum intermediate result, drop this branch.\n    |- Try 92 \/ 36 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (92, 12) (numbers left: [36]). Try possible operations.\n    |- Try 92 + 12 = 104. Add 104 to the number set. Current number set: [104, 36], target: 42, just two numbers left.\n     |- Try 104 + 36 = 140. Evaluate 140 != 42, drop this branch.\n     |- Try 104 - 36 = 68. Evaluate 68 != 42, drop this branch.\n     |- Try 104 * 36 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 36 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 92 - 12 = 80. Add 80 to the number set. Current number set: [80, 36], target: 42, just two numbers left.\n     |- Try 80 + 36 = 116. Evaluate 116 != 42, drop this branch.\n     |- Try 80 - 36 = 44. Evaluate 44 != 42, drop this branch.\n     |- Try 80 * 36 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 36 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 92 * 12 = 1104. Add 1104 to the number set. Current number set: [1104, 36], target: 42, just two numbers left.\n     |- Try 1104 + 36 = 1140. Evaluate 1140 != 42, drop this branch.\n     |- Try 1104 - 36 = 1068. Evaluate 1068 != 42, drop this branch.\n     |- Try 1104 * 36 = 39744. 39744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1104 \/ 36 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 92 \/ 12 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (36, 12) (numbers left: [92]). Try possible operations.\n    |- Try 36 + 12 = 48. Add 48 to the number set. Current number set: [48, 92], target: 42, just two numbers left.\n     |- Try 92 + 48 = 140. Evaluate 140 != 42, drop this branch.\n     |- Try 92 - 48 = 44. Evaluate 44 != 42, drop this branch.\n     |- Try 92 * 48 = 4416. 4416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 48 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 - 12 = 24. Add 24 to the number set. Current number set: [24, 92], target: 42, just two numbers left.\n     |- Try 92 + 24 = 116. Evaluate 116 != 42, drop this branch.\n     |- Try 92 - 24 = 68. Evaluate 68 != 42, drop this branch.\n     |- Try 92 * 24 = 2208. 2208 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 24 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 36 * 12 = 432. Add 432 to the number set. Current number set: [432, 92], target: 42, just two numbers left.\n     |- Try 432 + 92 = 524. Evaluate 524 != 42, drop this branch.\n     |- Try 432 - 92 = 340. Evaluate 340 != 42, drop this branch.\n     |- Try 432 * 92 = 39744. 39744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 92 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 36 \/ 12 = 3. Add 3 to the number set. Current number set: [3, 92], target: 42, just two numbers left.\n     |- Try 92 + 3 = 95. Evaluate 95 != 42, drop this branch.\n     |- Try 92 - 3 = 89. Evaluate 89 != 42, drop this branch.\n     |- Try 92 * 3 = 276. Evaluate 276 != 42, drop this branch.\n     |- Try 92 \/ 3 = 30.7. 30.7 is a decimal, drop this branch.\n  |- Try 49 - 43 = 6. Add 6 to the number set. Current number set: [6, 36, 12], target: 42. Options for choosing two numbers: [(6, 36), (6, 12), (36, 12)].\n   |- Pick two numbers (6, 36) (numbers left: [12]). Try possible operations.\n    |- Try 36 + 6 = 42. Add 42 to the number set. Current number set: [42, 12], target: 42, just two numbers left.\n     |- Try 42 + 12 = 54. Evaluate 54 != 42, drop this branch.\n     |- Try 42 - 12 = 30. Evaluate 30 != 42, drop this branch.\n     |- Try 42 * 12 = 504. Evaluate 504 != 42, drop this branch.\n     |- Try 42 \/ 12 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 36 - 6 = 30. Add 30 to the number set. Current number set: [30, 12], target: 42, just two numbers left.\n     |- Try 30 + 12 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 + 12 = 42\nThe step before: 36 - 6 = 30\nThe first step: 49 - 43 = 6\n\nOutput the solution in the required format:\n<Solution>\n49 - 43 = 6\n36 - 6 = 30\n30 + 12 = 42\n<\/Solution>\n","item":{"nums":[43,49,36,12],"solution":["49 - 43 = 6","36 - 6 = 30","30 + 12 = 42"],"target":42}}
+{"instance_id":"countdown_2k_110","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [14, 27, 18, 19]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [14, 27, 18, 19], target: 50. Options for choosing two numbers: [(14, 27), (14, 18), (14, 19), (27, 18), (27, 19), (18, 19)].\n |- Pick two numbers (14, 27) (numbers left: [18, 19]). Try possible operations.\n  |- Try 27 + 14 = 41. Add 41 to the number set. Current number set: [41, 18, 19], target: 50. Options for choosing two numbers: [(41, 18), (41, 19), (18, 19)].\n   |- Pick two numbers (41, 18) (numbers left: [19]). Try possible operations.\n    |- Try 41 + 18 = 59. Add 59 to the number set. Current number set: [59, 19], target: 50, just two numbers left.\n     |- Try 59 + 19 = 78. Evaluate 78 != 50, drop this branch.\n     |- Try 59 - 19 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 59 * 19 = 1121. Evaluate 1121 != 50, drop this branch.\n     |- Try 59 \/ 19 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 41 - 18 = 23. Add 23 to the number set. Current number set: [23, 19], target: 50, just two numbers left.\n     |- Try 23 + 19 = 42. Evaluate 42 != 50, drop this branch.\n     |- Try 23 - 19 = 4. Evaluate 4 != 50, drop this branch.\n     |- Try 23 * 19 = 437. Evaluate 437 != 50, drop this branch.\n     |- Try 23 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 18 = 738. Add 738 to the number set. Current number set: [738, 19], target: 50, just two numbers left.\n     |- Try 738 + 19 = 757. Evaluate 757 != 50, drop this branch.\n     |- Try 738 - 19 = 719. Evaluate 719 != 50, drop this branch.\n     |- Try 738 * 19 = 14022. 14022 exceeds the maximum intermediate result, drop this branch.\n     |- Try 738 \/ 19 = 38.8. 38.8 is a decimal, drop this branch.\n    |- Try 41 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (41, 19) (numbers left: [18]). Try possible operations.\n    |- Try 41 + 19 = 60. Add 60 to the number set. Current number set: [60, 18], target: 50, just two numbers left.\n     |- Try 60 + 18 = 78. Evaluate 78 != 50, drop this branch.\n     |- Try 60 - 18 = 42. Evaluate 42 != 50, drop this branch.\n     |- Try 60 * 18 = 1080. Evaluate 1080 != 50, drop this branch.\n     |- Try 60 \/ 18 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 41 - 19 = 22. Add 22 to the number set. Current number set: [22, 18], target: 50, just two numbers left.\n     |- Try 22 + 18 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 22 - 18 = 4. Evaluate 4 != 50, drop this branch.\n     |- Try 22 * 18 = 396. Evaluate 396 != 50, drop this branch.\n     |- Try 22 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 19 = 779. Add 779 to the number set. Current number set: [779, 18], target: 50, just two numbers left.\n     |- Try 779 + 18 = 797. Evaluate 797 != 50, drop this branch.\n     |- Try 779 - 18 = 761. Evaluate 761 != 50, drop this branch.\n     |- Try 779 * 18 = 14022. 14022 exceeds the maximum intermediate result, drop this branch.\n     |- Try 779 \/ 18 = 43.3. 43.3 is a decimal, drop this branch.\n    |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (18, 19) (numbers left: [41]). Try possible operations.\n    |- Try 19 + 18 = 37. Add 37 to the number set. Current number set: [37, 41], target: 50, just two numbers left.\n     |- Try 41 + 37 = 78. Evaluate 78 != 50, drop this branch.\n     |- Try 41 - 37 = 4. Evaluate 4 != 50, drop this branch.\n     |- Try 41 * 37 = 1517. Evaluate 1517 != 50, drop this branch.\n     |- Try 41 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 19 - 18 = 1. Add 1 to the number set. Current number set: [1, 41], target: 50, just two numbers left.\n     |- Try 41 + 1 = 42. Evaluate 42 != 50, drop this branch.\n     |- Try 41 - 1 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 41 * 1 = 41. Evaluate 41 != 50, drop this branch.\n     |- Try 41 \/ 1 = 41. Evaluate 41 != 50, drop this branch.\n    |- Try 19 * 18 = 342. Add 342 to the number set. Current number set: [342, 41], target: 50, just two numbers left.\n     |- Try 342 + 41 = 383. Evaluate 383 != 50, drop this branch.\n     |- Try 342 - 41 = 301. Evaluate 301 != 50, drop this branch.\n     |- Try 342 * 41 = 14022. 14022 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 41 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 27 - 14 = 13. Add 13 to the number set. Current number set: [13, 18, 19], target: 50. Options for choosing two numbers: [(13, 18), (13, 19), (18, 19)].\n   |- Pick two numbers (13, 18) (numbers left: [19]). Try possible operations.\n    |- Try 18 + 13 = 31. Add 31 to the number set. Current number set: [31, 19], target: 50, just two numbers left.\n     |- Try 31 + 19 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 + 19 = 50\nThe step before: 18 + 13 = 31\nThe first step: 27 - 14 = 13\n\nOutput the solution in the required format:\n<Solution>\n27 - 14 = 13\n18 + 13 = 31\n31 + 19 = 50\n<\/Solution>\n","item":{"nums":[14,27,18,19],"solution":["27 - 14 = 13","18 + 13 = 31","31 + 19 = 50"],"target":50}}
+{"instance_id":"countdown_2k_111","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 16, 8, 10]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [26, 16, 8, 10], target: 20. Options for choosing two numbers: [(26, 16), (26, 8), (26, 10), (16, 8), (16, 10), (8, 10)].\n |- Pick two numbers (26, 16) (numbers left: [8, 10]). Try possible operations.\n  |- Try 26 + 16 = 42. Add 42 to the number set. Current number set: [42, 8, 10], target: 20. Options for choosing two numbers: [(42, 8), (42, 10), (8, 10)].\n   |- Pick two numbers (42, 8) (numbers left: [10]). Try possible operations.\n    |- Try 42 + 8 = 50. Add 50 to the number set. Current number set: [50, 10], target: 20, just two numbers left.\n     |- Try 50 + 10 = 60. Evaluate 60 != 20, drop this branch.\n     |- Try 50 - 10 = 40. Evaluate 40 != 20, drop this branch.\n     |- Try 50 * 10 = 500. Evaluate 500 != 20, drop this branch.\n     |- Try 50 \/ 10 = 5. Evaluate 5 != 20, drop this branch.\n    |- Try 42 - 8 = 34. Add 34 to the number set. Current number set: [34, 10], target: 20, just two numbers left.\n     |- Try 34 + 10 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 34 - 10 = 24. Evaluate 24 != 20, drop this branch.\n     |- Try 34 * 10 = 340. Evaluate 340 != 20, drop this branch.\n     |- Try 34 \/ 10 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 42 * 8 = 336. Add 336 to the number set. Current number set: [336, 10], target: 20, just two numbers left.\n     |- Try 336 + 10 = 346. Evaluate 346 != 20, drop this branch.\n     |- Try 336 - 10 = 326. Evaluate 326 != 20, drop this branch.\n     |- Try 336 * 10 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 336 \/ 10 = 33.6. 33.6 is a decimal, drop this branch.\n    |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 10) (numbers left: [8]). Try possible operations.\n    |- Try 42 + 10 = 52. Add 52 to the number set. Current number set: [52, 8], target: 20, just two numbers left.\n     |- Try 52 + 8 = 60. Evaluate 60 != 20, drop this branch.\n     |- Try 52 - 8 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 52 * 8 = 416. Evaluate 416 != 20, drop this branch.\n     |- Try 52 \/ 8 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 42 - 10 = 32. Add 32 to the number set. Current number set: [32, 8], target: 20, just two numbers left.\n     |- Try 32 + 8 = 40. Evaluate 40 != 20, drop this branch.\n     |- Try 32 - 8 = 24. Evaluate 24 != 20, drop this branch.\n     |- Try 32 * 8 = 256. Evaluate 256 != 20, drop this branch.\n     |- Try 32 \/ 8 = 4. Evaluate 4 != 20, drop this branch.\n    |- Try 42 * 10 = 420. Add 420 to the number set. Current number set: [420, 8], target: 20, just two numbers left.\n     |- Try 420 + 8 = 428. Evaluate 428 != 20, drop this branch.\n     |- Try 420 - 8 = 412. Evaluate 412 != 20, drop this branch.\n     |- Try 420 * 8 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 8 = 52.5. 52.5 is a decimal, drop this branch.\n    |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 10) (numbers left: [42]). Try possible operations.\n    |- Try 10 + 8 = 18. Add 18 to the number set. Current number set: [18, 42], target: 20, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 20, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 20, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 20, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 10 - 8 = 2. Add 2 to the number set. Current number set: [2, 42], target: 20, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 42 - 2 = 40. Evaluate 40 != 20, drop this branch.\n     |- Try 42 * 2 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 42 \/ 2 = 21. Evaluate 21 != 20, drop this branch.\n    |- Try 10 * 8 = 80. Add 80 to the number set. Current number set: [80, 42], target: 20, just two numbers left.\n     |- Try 80 + 42 = 122. Evaluate 122 != 20, drop this branch.\n     |- Try 80 - 42 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 80 * 42 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 42 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 26 - 16 = 10. Add 10 to the number set. Current number set: [10, 8, 10], target: 20. Options for choosing two numbers: [(10, 8), (10, 10), (8, 10)].\n   |- Pick two numbers (10, 8) (numbers left: [10]). Try possible operations.\n    |- Try 10 + 8 = 18. Add 18 to the number set. Current number set: [18, 10], target: 20, just two numbers left.\n     |- Try 18 + 10 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 18 - 10 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 18 * 10 = 180. Evaluate 180 != 20, drop this branch.\n     |- Try 18 \/ 10 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 10 - 8 = 2. Add 2 to the number set. Current number set: [2, 10], target: 20, just two numbers left.\n     |- Try 10 + 2 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 10 - 2 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 10 * 2 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 10 * 2 = 20\nThe step before: 10 - 8 = 2\nThe first step: 26 - 16 = 10\n\nOutput the solution in the required format:\n<Solution>\n26 - 16 = 10\n10 - 8 = 2\n10 * 2 = 20\n<\/Solution>\n","item":{"nums":[26,16,8,10],"solution":["26 - 16 = 10","10 - 8 = 2","10 * 2 = 20"],"target":20}}
+{"instance_id":"countdown_2k_112","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [21, 42, 27, 3]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [21, 42, 27, 3], target: 48. Options for choosing two numbers: [(21, 42), (21, 27), (21, 3), (42, 27), (42, 3), (27, 3)].\n |- Pick two numbers (21, 42) (numbers left: [27, 3]). Try possible operations.\n  |- Try 42 + 21 = 63. Add 63 to the number set. Current number set: [63, 27, 3], target: 48. Options for choosing two numbers: [(63, 27), (63, 3), (27, 3)].\n   |- Pick two numbers (63, 27) (numbers left: [3]). Try possible operations.\n    |- Try 63 + 27 = 90. Add 90 to the number set. Current number set: [90, 3], target: 48, just two numbers left.\n     |- Try 90 + 3 = 93. Evaluate 93 != 48, drop this branch.\n     |- Try 90 - 3 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 90 * 3 = 270. Evaluate 270 != 48, drop this branch.\n     |- Try 90 \/ 3 = 30. Evaluate 30 != 48, drop this branch.\n    |- Try 63 - 27 = 36. Add 36 to the number set. Current number set: [36, 3], target: 48, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 48, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 36 * 3 = 108. Evaluate 108 != 48, drop this branch.\n     |- Try 36 \/ 3 = 12. Evaluate 12 != 48, drop this branch.\n    |- Try 63 * 27 = 1701. Add 1701 to the number set. Current number set: [1701, 3], target: 48, just two numbers left.\n     |- Try 1701 + 3 = 1704. Evaluate 1704 != 48, drop this branch.\n     |- Try 1701 - 3 = 1698. Evaluate 1698 != 48, drop this branch.\n     |- Try 1701 * 3 = 5103. 5103 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1701 \/ 3 = 567. Evaluate 567 != 48, drop this branch.\n    |- Try 63 \/ 27 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (63, 3) (numbers left: [27]). Try possible operations.\n    |- Try 63 + 3 = 66. Add 66 to the number set. Current number set: [66, 27], target: 48, just two numbers left.\n     |- Try 66 + 27 = 93. Evaluate 93 != 48, drop this branch.\n     |- Try 66 - 27 = 39. Evaluate 39 != 48, drop this branch.\n     |- Try 66 * 27 = 1782. Evaluate 1782 != 48, drop this branch.\n     |- Try 66 \/ 27 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 63 - 3 = 60. Add 60 to the number set. Current number set: [60, 27], target: 48, just two numbers left.\n     |- Try 60 + 27 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 60 - 27 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 60 * 27 = 1620. Evaluate 1620 != 48, drop this branch.\n     |- Try 60 \/ 27 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 63 * 3 = 189. Add 189 to the number set. Current number set: [189, 27], target: 48, just two numbers left.\n     |- Try 189 + 27 = 216. Evaluate 216 != 48, drop this branch.\n     |- Try 189 - 27 = 162. Evaluate 162 != 48, drop this branch.\n     |- Try 189 * 27 = 5103. 5103 exceeds the maximum intermediate result, drop this branch.\n     |- Try 189 \/ 27 = 7. Evaluate 7 != 48, drop this branch.\n    |- Try 63 \/ 3 = 21. Add 21 to the number set. Current number set: [21, 27], target: 48, just two numbers left.\n     |- Try 27 + 21 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 21 = 48\nThe step before: 63 \/ 3 = 21\nThe first step: 42 + 21 = 63\n\nOutput the solution in the required format:\n<Solution>\n42 + 21 = 63\n63 \/ 3 = 21\n27 + 21 = 48\n<\/Solution>\n","item":{"nums":[21,42,27,3],"solution":["42 + 21 = 63","63 \/ 3 = 21","27 + 21 = 48"],"target":48}}
+{"instance_id":"countdown_2k_113","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 45, 2, 49]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [30, 45, 2, 49], target: 36. Options for choosing two numbers: [(30, 45), (30, 2), (30, 49), (45, 2), (45, 49), (2, 49)].\n |- Pick two numbers (30, 45) (numbers left: [2, 49]). Try possible operations.\n  |- Try 45 + 30 = 75. Add 75 to the number set. Current number set: [75, 2, 49], target: 36. Options for choosing two numbers: [(75, 2), (75, 49), (2, 49)].\n   |- Pick two numbers (75, 2) (numbers left: [49]). Try possible operations.\n    |- Try 75 + 2 = 77. Add 77 to the number set. Current number set: [77, 49], target: 36, just two numbers left.\n     |- Try 77 + 49 = 126. Evaluate 126 != 36, drop this branch.\n     |- Try 77 - 49 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 77 * 49 = 3773. 3773 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 75 - 2 = 73. Add 73 to the number set. Current number set: [73, 49], target: 36, just two numbers left.\n     |- Try 73 + 49 = 122. Evaluate 122 != 36, drop this branch.\n     |- Try 73 - 49 = 24. Evaluate 24 != 36, drop this branch.\n     |- Try 73 * 49 = 3577. 3577 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 49 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 75 * 2 = 150. Add 150 to the number set. Current number set: [150, 49], target: 36, just two numbers left.\n     |- Try 150 + 49 = 199. Evaluate 199 != 36, drop this branch.\n     |- Try 150 - 49 = 101. Evaluate 101 != 36, drop this branch.\n     |- Try 150 * 49 = 7350. 7350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 49 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 75 \/ 2 = 37.5. 37.5 is a decimal, drop this branch.\n   |- Pick two numbers (75, 49) (numbers left: [2]). Try possible operations.\n    |- Try 75 + 49 = 124. Add 124 to the number set. Current number set: [124, 2], target: 36, just two numbers left.\n     |- Try 124 + 2 = 126. Evaluate 126 != 36, drop this branch.\n     |- Try 124 - 2 = 122. Evaluate 122 != 36, drop this branch.\n     |- Try 124 * 2 = 248. Evaluate 248 != 36, drop this branch.\n     |- Try 124 \/ 2 = 62. Evaluate 62 != 36, drop this branch.\n    |- Try 75 - 49 = 26. Add 26 to the number set. Current number set: [26, 2], target: 36, just two numbers left.\n     |- Try 26 + 2 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 26 - 2 = 24. Evaluate 24 != 36, drop this branch.\n     |- Try 26 * 2 = 52. Evaluate 52 != 36, drop this branch.\n     |- Try 26 \/ 2 = 13. Evaluate 13 != 36, drop this branch.\n    |- Try 75 * 49 = 3675. 3675 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 49 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 49) (numbers left: [75]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 75], target: 36, just two numbers left.\n     |- Try 75 + 51 = 126. Evaluate 126 != 36, drop this branch.\n     |- Try 75 - 51 = 24. Evaluate 24 != 36, drop this branch.\n     |- Try 75 * 51 = 3825. 3825 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 51 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 75], target: 36, just two numbers left.\n     |- Try 75 + 47 = 122. Evaluate 122 != 36, drop this branch.\n     |- Try 75 - 47 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 75 * 47 = 3525. 3525 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 47 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 75], target: 36, just two numbers left.\n     |- Try 98 + 75 = 173. Evaluate 173 != 36, drop this branch.\n     |- Try 98 - 75 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 98 * 75 = 7350. 7350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 75 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n  |- Try 45 - 30 = 15. Add 15 to the number set. Current number set: [15, 2, 49], target: 36. Options for choosing two numbers: [(15, 2), (15, 49), (2, 49)].\n   |- Pick two numbers (15, 2) (numbers left: [49]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 49], target: 36, just two numbers left.\n     |- Try 49 + 17 = 66. Evaluate 66 != 36, drop this branch.\n     |- Try 49 - 17 = 32. Evaluate 32 != 36, drop this branch.\n     |- Try 49 * 17 = 833. Evaluate 833 != 36, drop this branch.\n     |- Try 49 \/ 17 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 49], target: 36, just two numbers left.\n     |- Try 49 + 13 = 62. Evaluate 62 != 36, drop this branch.\n     |- Try 49 - 13 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 - 13 = 36\nThe step before: 15 - 2 = 13\nThe first step: 45 - 30 = 15\n\nOutput the solution in the required format:\n<Solution>\n45 - 30 = 15\n15 - 2 = 13\n49 - 13 = 36\n<\/Solution>\n","item":{"nums":[30,45,2,49],"solution":["45 - 30 = 15","15 - 2 = 13","49 - 13 = 36"],"target":36}}
+{"instance_id":"countdown_2k_114","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [21, 29, 31, 48]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [21, 29, 31, 48], target: 25. Options for choosing two numbers: [(21, 29), (21, 31), (21, 48), (29, 31), (29, 48), (31, 48)].\n |- Pick two numbers (21, 29) (numbers left: [31, 48]). Try possible operations.\n  |- Try 29 + 21 = 50. Add 50 to the number set. Current number set: [50, 31, 48], target: 25. Options for choosing two numbers: [(50, 31), (50, 48), (31, 48)].\n   |- Pick two numbers (50, 31) (numbers left: [48]). Try possible operations.\n    |- Try 50 + 31 = 81. Add 81 to the number set. Current number set: [81, 48], target: 25, just two numbers left.\n     |- Try 81 + 48 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 81 - 48 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 81 * 48 = 3888. 3888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 48 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 50 - 31 = 19. Add 19 to the number set. Current number set: [19, 48], target: 25, just two numbers left.\n     |- Try 48 + 19 = 67. Evaluate 67 != 25, drop this branch.\n     |- Try 48 - 19 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 48 * 19 = 912. Evaluate 912 != 25, drop this branch.\n     |- Try 48 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 50 * 31 = 1550. Add 1550 to the number set. Current number set: [1550, 48], target: 25, just two numbers left.\n     |- Try 1550 + 48 = 1598. Evaluate 1598 != 25, drop this branch.\n     |- Try 1550 - 48 = 1502. Evaluate 1502 != 25, drop this branch.\n     |- Try 1550 * 48 = 74400. 74400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1550 \/ 48 = 32.3. 32.3 is a decimal, drop this branch.\n    |- Try 50 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (50, 48) (numbers left: [31]). Try possible operations.\n    |- Try 50 + 48 = 98. Add 98 to the number set. Current number set: [98, 31], target: 25, just two numbers left.\n     |- Try 98 + 31 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 98 - 31 = 67. Evaluate 67 != 25, drop this branch.\n     |- Try 98 * 31 = 3038. 3038 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 31 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 50 - 48 = 2. Add 2 to the number set. Current number set: [2, 31], target: 25, just two numbers left.\n     |- Try 31 + 2 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 31 - 2 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 31 * 2 = 62. Evaluate 62 != 25, drop this branch.\n     |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 50 * 48 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 48 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (31, 48) (numbers left: [50]). Try possible operations.\n    |- Try 48 + 31 = 79. Add 79 to the number set. Current number set: [79, 50], target: 25, just two numbers left.\n     |- Try 79 + 50 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 79 - 50 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 79 * 50 = 3950. 3950 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 50 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 48 - 31 = 17. Add 17 to the number set. Current number set: [17, 50], target: 25, just two numbers left.\n     |- Try 50 + 17 = 67. Evaluate 67 != 25, drop this branch.\n     |- Try 50 - 17 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 50 * 17 = 850. Evaluate 850 != 25, drop this branch.\n     |- Try 50 \/ 17 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 48 * 31 = 1488. Add 1488 to the number set. Current number set: [1488, 50], target: 25, just two numbers left.\n     |- Try 1488 + 50 = 1538. Evaluate 1538 != 25, drop this branch.\n     |- Try 1488 - 50 = 1438. Evaluate 1438 != 25, drop this branch.\n     |- Try 1488 * 50 = 74400. 74400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1488 \/ 50 = 29.8. 29.8 is a decimal, drop this branch.\n    |- Try 48 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 29 - 21 = 8. Add 8 to the number set. Current number set: [8, 31, 48], target: 25. Options for choosing two numbers: [(8, 31), (8, 48), (31, 48)].\n   |- Pick two numbers (8, 31) (numbers left: [48]). Try possible operations.\n    |- Try 31 + 8 = 39. Add 39 to the number set. Current number set: [39, 48], target: 25, just two numbers left.\n     |- Try 48 + 39 = 87. Evaluate 87 != 25, drop this branch.\n     |- Try 48 - 39 = 9. Evaluate 9 != 25, drop this branch.\n     |- Try 48 * 39 = 1872. Evaluate 1872 != 25, drop this branch.\n     |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 - 8 = 23. Add 23 to the number set. Current number set: [23, 48], target: 25, just two numbers left.\n     |- Try 48 + 23 = 71. Evaluate 71 != 25, drop this branch.\n     |- Try 48 - 23 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 23 = 25\nThe step before: 31 - 8 = 23\nThe first step: 29 - 21 = 8\n\nOutput the solution in the required format:\n<Solution>\n29 - 21 = 8\n31 - 8 = 23\n48 - 23 = 25\n<\/Solution>\n","item":{"nums":[21,29,31,48],"solution":["29 - 21 = 8","31 - 8 = 23","48 - 23 = 25"],"target":25}}
+{"instance_id":"countdown_2k_115","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 10, 6, 24]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [17, 10, 6, 24], target: 11. Options for choosing two numbers: [(17, 10), (17, 6), (17, 24), (10, 6), (10, 24), (6, 24)].\n |- Pick two numbers (17, 10) (numbers left: [6, 24]). Try possible operations.\n  |- Try 17 + 10 = 27. Add 27 to the number set. Current number set: [27, 6, 24], target: 11. Options for choosing two numbers: [(27, 6), (27, 24), (6, 24)].\n   |- Pick two numbers (27, 6) (numbers left: [24]). Try possible operations.\n    |- Try 27 + 6 = 33. Add 33 to the number set. Current number set: [33, 24], target: 11, just two numbers left.\n     |- Try 33 + 24 = 57. Evaluate 57 != 11, drop this branch.\n     |- Try 33 - 24 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 33 * 24 = 792. Evaluate 792 != 11, drop this branch.\n     |- Try 33 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 - 6 = 21. Add 21 to the number set. Current number set: [21, 24], target: 11, just two numbers left.\n     |- Try 24 + 21 = 45. Evaluate 45 != 11, drop this branch.\n     |- Try 24 - 21 = 3. Evaluate 3 != 11, drop this branch.\n     |- Try 24 * 21 = 504. Evaluate 504 != 11, drop this branch.\n     |- Try 24 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 * 6 = 162. Add 162 to the number set. Current number set: [162, 24], target: 11, just two numbers left.\n     |- Try 162 + 24 = 186. Evaluate 186 != 11, drop this branch.\n     |- Try 162 - 24 = 138. Evaluate 138 != 11, drop this branch.\n     |- Try 162 * 24 = 3888. 3888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 24 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (27, 24) (numbers left: [6]). Try possible operations.\n    |- Try 27 + 24 = 51. Add 51 to the number set. Current number set: [51, 6], target: 11, just two numbers left.\n     |- Try 51 + 6 = 57. Evaluate 57 != 11, drop this branch.\n     |- Try 51 - 6 = 45. Evaluate 45 != 11, drop this branch.\n     |- Try 51 * 6 = 306. Evaluate 306 != 11, drop this branch.\n     |- Try 51 \/ 6 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 27 - 24 = 3. Add 3 to the number set. Current number set: [3, 6], target: 11, just two numbers left.\n     |- Try 6 + 3 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 6 - 3 = 3. Evaluate 3 != 11, drop this branch.\n     |- Try 6 * 3 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 6 \/ 3 = 2. Evaluate 2 != 11, drop this branch.\n    |- Try 27 * 24 = 648. Add 648 to the number set. Current number set: [648, 6], target: 11, just two numbers left.\n     |- Try 648 + 6 = 654. Evaluate 654 != 11, drop this branch.\n     |- Try 648 - 6 = 642. Evaluate 642 != 11, drop this branch.\n     |- Try 648 * 6 = 3888. 3888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 6 = 108. Evaluate 108 != 11, drop this branch.\n    |- Try 27 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (6, 24) (numbers left: [27]). Try possible operations.\n    |- Try 24 + 6 = 30. Add 30 to the number set. Current number set: [30, 27], target: 11, just two numbers left.\n     |- Try 30 + 27 = 57. Evaluate 57 != 11, drop this branch.\n     |- Try 30 - 27 = 3. Evaluate 3 != 11, drop this branch.\n     |- Try 30 * 27 = 810. Evaluate 810 != 11, drop this branch.\n     |- Try 30 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 6 = 18. Add 18 to the number set. Current number set: [18, 27], target: 11, just two numbers left.\n     |- Try 27 + 18 = 45. Evaluate 45 != 11, drop this branch.\n     |- Try 27 - 18 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 27 * 18 = 486. Evaluate 486 != 11, drop this branch.\n     |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 * 6 = 144. Add 144 to the number set. Current number set: [144, 27], target: 11, just two numbers left.\n     |- Try 144 + 27 = 171. Evaluate 171 != 11, drop this branch.\n     |- Try 144 - 27 = 117. Evaluate 117 != 11, drop this branch.\n     |- Try 144 * 27 = 3888. 3888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 27 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 24 \/ 6 = 4. Add 4 to the number set. Current number set: [4, 27], target: 11, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 11, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 11, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 11, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n  |- Try 17 - 10 = 7. Add 7 to the number set. Current number set: [7, 6, 24], target: 11. Options for choosing two numbers: [(7, 6), (7, 24), (6, 24)].\n   |- Pick two numbers (7, 6) (numbers left: [24]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 24], target: 11, just two numbers left.\n     |- Try 24 + 13 = 37. Evaluate 37 != 11, drop this branch.\n     |- Try 24 - 13 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 - 13 = 11\nThe step before: 7 + 6 = 13\nThe first step: 17 - 10 = 7\n\nOutput the solution in the required format:\n<Solution>\n17 - 10 = 7\n7 + 6 = 13\n24 - 13 = 11\n<\/Solution>\n","item":{"nums":[17,10,6,24],"solution":["17 - 10 = 7","7 + 6 = 13","24 - 13 = 11"],"target":11}}
+{"instance_id":"countdown_2k_116","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [34, 28, 30, 44]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [34, 28, 30, 44], target: 20. Options for choosing two numbers: [(34, 28), (34, 30), (34, 44), (28, 30), (28, 44), (30, 44)].\n |- Pick two numbers (34, 28) (numbers left: [30, 44]). Try possible operations.\n  |- Try 34 + 28 = 62. Add 62 to the number set. Current number set: [62, 30, 44], target: 20. Options for choosing two numbers: [(62, 30), (62, 44), (30, 44)].\n   |- Pick two numbers (62, 30) (numbers left: [44]). Try possible operations.\n    |- Try 62 + 30 = 92. Add 92 to the number set. Current number set: [92, 44], target: 20, just two numbers left.\n     |- Try 92 + 44 = 136. Evaluate 136 != 20, drop this branch.\n     |- Try 92 - 44 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 92 * 44 = 4048. 4048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 44 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 62 - 30 = 32. Add 32 to the number set. Current number set: [32, 44], target: 20, just two numbers left.\n     |- Try 44 + 32 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 44 - 32 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 44 * 32 = 1408. Evaluate 1408 != 20, drop this branch.\n     |- Try 44 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 62 * 30 = 1860. Add 1860 to the number set. Current number set: [1860, 44], target: 20, just two numbers left.\n     |- Try 1860 + 44 = 1904. Evaluate 1904 != 20, drop this branch.\n     |- Try 1860 - 44 = 1816. Evaluate 1816 != 20, drop this branch.\n     |- Try 1860 * 44 = 81840. 81840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1860 \/ 44 = 42.3. 42.3 is a decimal, drop this branch.\n    |- Try 62 \/ 30 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (62, 44) (numbers left: [30]). Try possible operations.\n    |- Try 62 + 44 = 106. Add 106 to the number set. Current number set: [106, 30], target: 20, just two numbers left.\n     |- Try 106 + 30 = 136. Evaluate 136 != 20, drop this branch.\n     |- Try 106 - 30 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 106 * 30 = 3180. 3180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 106 \/ 30 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 62 - 44 = 18. Add 18 to the number set. Current number set: [18, 30], target: 20, just two numbers left.\n     |- Try 30 + 18 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 30 - 18 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 30 * 18 = 540. Evaluate 540 != 20, drop this branch.\n     |- Try 30 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 62 * 44 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (30, 44) (numbers left: [62]). Try possible operations.\n    |- Try 44 + 30 = 74. Add 74 to the number set. Current number set: [74, 62], target: 20, just two numbers left.\n     |- Try 74 + 62 = 136. Evaluate 136 != 20, drop this branch.\n     |- Try 74 - 62 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 74 * 62 = 4588. 4588 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 62 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 - 30 = 14. Add 14 to the number set. Current number set: [14, 62], target: 20, just two numbers left.\n     |- Try 62 + 14 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 62 - 14 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 62 * 14 = 868. Evaluate 868 != 20, drop this branch.\n     |- Try 62 \/ 14 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 44 * 30 = 1320. Add 1320 to the number set. Current number set: [1320, 62], target: 20, just two numbers left.\n     |- Try 1320 + 62 = 1382. Evaluate 1382 != 20, drop this branch.\n     |- Try 1320 - 62 = 1258. Evaluate 1258 != 20, drop this branch.\n     |- Try 1320 * 62 = 81840. 81840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1320 \/ 62 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 44 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 34 - 28 = 6. Add 6 to the number set. Current number set: [6, 30, 44], target: 20. Options for choosing two numbers: [(6, 30), (6, 44), (30, 44)].\n   |- Pick two numbers (6, 30) (numbers left: [44]). Try possible operations.\n    |- Try 30 + 6 = 36. Add 36 to the number set. Current number set: [36, 44], target: 20, just two numbers left.\n     |- Try 44 + 36 = 80. Evaluate 80 != 20, drop this branch.\n     |- Try 44 - 36 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 44 * 36 = 1584. Evaluate 1584 != 20, drop this branch.\n     |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 - 6 = 24. Add 24 to the number set. Current number set: [24, 44], target: 20, just two numbers left.\n     |- Try 44 + 24 = 68. Evaluate 68 != 20, drop this branch.\n     |- Try 44 - 24 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 24 = 20\nThe step before: 30 - 6 = 24\nThe first step: 34 - 28 = 6\n\nOutput the solution in the required format:\n<Solution>\n34 - 28 = 6\n30 - 6 = 24\n44 - 24 = 20\n<\/Solution>\n","item":{"nums":[34,28,30,44],"solution":["34 - 28 = 6","30 - 6 = 24","44 - 24 = 20"],"target":20}}
+{"instance_id":"countdown_2k_117","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 30, 9, 6]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [22, 30, 9, 6], target: 23. Options for choosing two numbers: [(22, 30), (22, 9), (22, 6), (30, 9), (30, 6), (9, 6)].\n |- Pick two numbers (22, 30) (numbers left: [9, 6]). Try possible operations.\n  |- Try 30 + 22 = 52. Add 52 to the number set. Current number set: [52, 9, 6], target: 23. Options for choosing two numbers: [(52, 9), (52, 6), (9, 6)].\n   |- Pick two numbers (52, 9) (numbers left: [6]). Try possible operations.\n    |- Try 52 + 9 = 61. Add 61 to the number set. Current number set: [61, 6], target: 23, just two numbers left.\n     |- Try 61 + 6 = 67. Evaluate 67 != 23, drop this branch.\n     |- Try 61 - 6 = 55. Evaluate 55 != 23, drop this branch.\n     |- Try 61 * 6 = 366. Evaluate 366 != 23, drop this branch.\n     |- Try 61 \/ 6 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 52 - 9 = 43. Add 43 to the number set. Current number set: [43, 6], target: 23, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 23, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 23, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 52 * 9 = 468. Add 468 to the number set. Current number set: [468, 6], target: 23, just two numbers left.\n     |- Try 468 + 6 = 474. Evaluate 474 != 23, drop this branch.\n     |- Try 468 - 6 = 462. Evaluate 462 != 23, drop this branch.\n     |- Try 468 * 6 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 6 = 78. Evaluate 78 != 23, drop this branch.\n    |- Try 52 \/ 9 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (52, 6) (numbers left: [9]). Try possible operations.\n    |- Try 52 + 6 = 58. Add 58 to the number set. Current number set: [58, 9], target: 23, just two numbers left.\n     |- Try 58 + 9 = 67. Evaluate 67 != 23, drop this branch.\n     |- Try 58 - 9 = 49. Evaluate 49 != 23, drop this branch.\n     |- Try 58 * 9 = 522. Evaluate 522 != 23, drop this branch.\n     |- Try 58 \/ 9 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 52 - 6 = 46. Add 46 to the number set. Current number set: [46, 9], target: 23, just two numbers left.\n     |- Try 46 + 9 = 55. Evaluate 55 != 23, drop this branch.\n     |- Try 46 - 9 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 46 * 9 = 414. Evaluate 414 != 23, drop this branch.\n     |- Try 46 \/ 9 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 52 * 6 = 312. Add 312 to the number set. Current number set: [312, 9], target: 23, just two numbers left.\n     |- Try 312 + 9 = 321. Evaluate 321 != 23, drop this branch.\n     |- Try 312 - 9 = 303. Evaluate 303 != 23, drop this branch.\n     |- Try 312 * 9 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 9 = 34.7. 34.7 is a decimal, drop this branch.\n    |- Try 52 \/ 6 = 8.7. 8.7 is a decimal, drop this branch.\n   |- Pick two numbers (9, 6) (numbers left: [52]). Try possible operations.\n    |- Try 9 + 6 = 15. Add 15 to the number set. Current number set: [15, 52], target: 23, just two numbers left.\n     |- Try 52 + 15 = 67. Evaluate 67 != 23, drop this branch.\n     |- Try 52 - 15 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 52 * 15 = 780. Evaluate 780 != 23, drop this branch.\n     |- Try 52 \/ 15 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 9 - 6 = 3. Add 3 to the number set. Current number set: [3, 52], target: 23, just two numbers left.\n     |- Try 52 + 3 = 55. Evaluate 55 != 23, drop this branch.\n     |- Try 52 - 3 = 49. Evaluate 49 != 23, drop this branch.\n     |- Try 52 * 3 = 156. Evaluate 156 != 23, drop this branch.\n     |- Try 52 \/ 3 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 9 * 6 = 54. Add 54 to the number set. Current number set: [54, 52], target: 23, just two numbers left.\n     |- Try 54 + 52 = 106. Evaluate 106 != 23, drop this branch.\n     |- Try 54 - 52 = 2. Evaluate 2 != 23, drop this branch.\n     |- Try 54 * 52 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 52 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 9 \/ 6 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 30 - 22 = 8. Add 8 to the number set. Current number set: [8, 9, 6], target: 23. Options for choosing two numbers: [(8, 9), (8, 6), (9, 6)].\n   |- Pick two numbers (8, 9) (numbers left: [6]). Try possible operations.\n    |- Try 9 + 8 = 17. Add 17 to the number set. Current number set: [17, 6], target: 23, just two numbers left.\n     |- Try 17 + 6 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 17 + 6 = 23\nThe step before: 9 + 8 = 17\nThe first step: 30 - 22 = 8\n\nOutput the solution in the required format:\n<Solution>\n30 - 22 = 8\n9 + 8 = 17\n17 + 6 = 23\n<\/Solution>\n","item":{"nums":[22,30,9,6],"solution":["30 - 22 = 8","9 + 8 = 17","17 + 6 = 23"],"target":23}}
+{"instance_id":"countdown_2k_118","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 34, 28, 10]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [46, 34, 28, 10], target: 30. Options for choosing two numbers: [(46, 34), (46, 28), (46, 10), (34, 28), (34, 10), (28, 10)].\n |- Pick two numbers (46, 34) (numbers left: [28, 10]). Try possible operations.\n  |- Try 46 + 34 = 80. Add 80 to the number set. Current number set: [80, 28, 10], target: 30. Options for choosing two numbers: [(80, 28), (80, 10), (28, 10)].\n   |- Pick two numbers (80, 28) (numbers left: [10]). Try possible operations.\n    |- Try 80 + 28 = 108. Add 108 to the number set. Current number set: [108, 10], target: 30, just two numbers left.\n     |- Try 108 + 10 = 118. Evaluate 118 != 30, drop this branch.\n     |- Try 108 - 10 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 108 * 10 = 1080. Evaluate 1080 != 30, drop this branch.\n     |- Try 108 \/ 10 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 80 - 28 = 52. Add 52 to the number set. Current number set: [52, 10], target: 30, just two numbers left.\n     |- Try 52 + 10 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 52 - 10 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 52 * 10 = 520. Evaluate 520 != 30, drop this branch.\n     |- Try 52 \/ 10 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 80 * 28 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n    |- Try 80 \/ 28 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (80, 10) (numbers left: [28]). Try possible operations.\n    |- Try 80 + 10 = 90. Add 90 to the number set. Current number set: [90, 28], target: 30, just two numbers left.\n     |- Try 90 + 28 = 118. Evaluate 118 != 30, drop this branch.\n     |- Try 90 - 28 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 90 * 28 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 28 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 80 - 10 = 70. Add 70 to the number set. Current number set: [70, 28], target: 30, just two numbers left.\n     |- Try 70 + 28 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 70 - 28 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 70 * 28 = 1960. Evaluate 1960 != 30, drop this branch.\n     |- Try 70 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 80 * 10 = 800. Add 800 to the number set. Current number set: [800, 28], target: 30, just two numbers left.\n     |- Try 800 + 28 = 828. Evaluate 828 != 30, drop this branch.\n     |- Try 800 - 28 = 772. Evaluate 772 != 30, drop this branch.\n     |- Try 800 * 28 = 22400. 22400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 28 = 28.6. 28.6 is a decimal, drop this branch.\n    |- Try 80 \/ 10 = 8. Add 8 to the number set. Current number set: [8, 28], target: 30, just two numbers left.\n     |- Try 28 + 8 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 28 - 8 = 20. Evaluate 20 != 30, drop this branch.\n     |- Try 28 * 8 = 224. Evaluate 224 != 30, drop this branch.\n     |- Try 28 \/ 8 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 10) (numbers left: [80]). Try possible operations.\n    |- Try 28 + 10 = 38. Add 38 to the number set. Current number set: [38, 80], target: 30, just two numbers left.\n     |- Try 80 + 38 = 118. Evaluate 118 != 30, drop this branch.\n     |- Try 80 - 38 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 80 * 38 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 38 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 28 - 10 = 18. Add 18 to the number set. Current number set: [18, 80], target: 30, just two numbers left.\n     |- Try 80 + 18 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 80 - 18 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 80 * 18 = 1440. Evaluate 1440 != 30, drop this branch.\n     |- Try 80 \/ 18 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 28 * 10 = 280. Add 280 to the number set. Current number set: [280, 80], target: 30, just two numbers left.\n     |- Try 280 + 80 = 360. Evaluate 360 != 30, drop this branch.\n     |- Try 280 - 80 = 200. Evaluate 200 != 30, drop this branch.\n     |- Try 280 * 80 = 22400. 22400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 80 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 28 \/ 10 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 46 - 34 = 12. Add 12 to the number set. Current number set: [12, 28, 10], target: 30. Options for choosing two numbers: [(12, 28), (12, 10), (28, 10)].\n   |- Pick two numbers (12, 28) (numbers left: [10]). Try possible operations.\n    |- Try 28 + 12 = 40. Add 40 to the number set. Current number set: [40, 10], target: 30, just two numbers left.\n     |- Try 40 + 10 = 50. Evaluate 50 != 30, drop this branch.\n     |- Try 40 - 10 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 - 10 = 30\nThe step before: 28 + 12 = 40\nThe first step: 46 - 34 = 12\n\nOutput the solution in the required format:\n<Solution>\n46 - 34 = 12\n28 + 12 = 40\n40 - 10 = 30\n<\/Solution>\n","item":{"nums":[46,34,28,10],"solution":["46 - 34 = 12","28 + 12 = 40","40 - 10 = 30"],"target":30}}
+{"instance_id":"countdown_2k_119","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 21, 3, 9]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [8, 21, 3, 9], target: 26. Options for choosing two numbers: [(8, 21), (8, 3), (8, 9), (21, 3), (21, 9), (3, 9)].\n |- Pick two numbers (8, 21) (numbers left: [3, 9]). Try possible operations.\n  |- Try 21 + 8 = 29. Add 29 to the number set. Current number set: [29, 3, 9], target: 26. Options for choosing two numbers: [(29, 3), (29, 9), (3, 9)].\n   |- Pick two numbers (29, 3) (numbers left: [9]). Try possible operations.\n    |- Try 29 + 3 = 32. Add 32 to the number set. Current number set: [32, 9], target: 26, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 26, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 26, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 26, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 29 - 3 = 26. Add 26 to the number set. Current number set: [26, 9], target: 26, just two numbers left.\n     |- Try 26 + 9 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 26 - 9 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 26 * 9 = 234. Evaluate 234 != 26, drop this branch.\n     |- Try 26 \/ 9 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 29 * 3 = 87. Add 87 to the number set. Current number set: [87, 9], target: 26, just two numbers left.\n     |- Try 87 + 9 = 96. Evaluate 96 != 26, drop this branch.\n     |- Try 87 - 9 = 78. Evaluate 78 != 26, drop this branch.\n     |- Try 87 * 9 = 783. Evaluate 783 != 26, drop this branch.\n     |- Try 87 \/ 9 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n   |- Pick two numbers (29, 9) (numbers left: [3]). Try possible operations.\n    |- Try 29 + 9 = 38. Add 38 to the number set. Current number set: [38, 3], target: 26, just two numbers left.\n     |- Try 38 + 3 = 41. Evaluate 41 != 26, drop this branch.\n     |- Try 38 - 3 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 38 * 3 = 114. Evaluate 114 != 26, drop this branch.\n     |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 29 - 9 = 20. Add 20 to the number set. Current number set: [20, 3], target: 26, just two numbers left.\n     |- Try 20 + 3 = 23. Evaluate 23 != 26, drop this branch.\n     |- Try 20 - 3 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 20 * 3 = 60. Evaluate 60 != 26, drop this branch.\n     |- Try 20 \/ 3 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 29 * 9 = 261. Add 261 to the number set. Current number set: [261, 3], target: 26, just two numbers left.\n     |- Try 261 + 3 = 264. Evaluate 264 != 26, drop this branch.\n     |- Try 261 - 3 = 258. Evaluate 258 != 26, drop this branch.\n     |- Try 261 * 3 = 783. Evaluate 783 != 26, drop this branch.\n     |- Try 261 \/ 3 = 87. Evaluate 87 != 26, drop this branch.\n    |- Try 29 \/ 9 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 9) (numbers left: [29]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 29], target: 26, just two numbers left.\n     |- Try 29 + 12 = 41. Evaluate 41 != 26, drop this branch.\n     |- Try 29 - 12 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 29 * 12 = 348. Evaluate 348 != 26, drop this branch.\n     |- Try 29 \/ 12 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 29], target: 26, just two numbers left.\n     |- Try 29 + 6 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 29 - 6 = 23. Evaluate 23 != 26, drop this branch.\n     |- Try 29 * 6 = 174. Evaluate 174 != 26, drop this branch.\n     |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 29], target: 26, just two numbers left.\n     |- Try 29 + 27 = 56. Evaluate 56 != 26, drop this branch.\n     |- Try 29 - 27 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 29 * 27 = 783. Evaluate 783 != 26, drop this branch.\n     |- Try 29 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 29], target: 26, just two numbers left.\n     |- Try 29 + 3 = 32. Evaluate 32 != 26, drop this branch.\n     |- Try 29 - 3 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 - 3 = 26\nThe step before: 9 \/ 3 = 3\nThe first step: 21 + 8 = 29\n\nOutput the solution in the required format:\n<Solution>\n21 + 8 = 29\n9 \/ 3 = 3\n29 - 3 = 26\n<\/Solution>\n","item":{"nums":[8,21,3,9],"solution":["21 + 8 = 29","9 \/ 3 = 3","29 - 3 = 26"],"target":26}}
+{"instance_id":"countdown_2k_120","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 15, 12, 3]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [4, 15, 12, 3], target: 20. Options for choosing two numbers: [(4, 15), (4, 12), (4, 3), (15, 12), (15, 3), (12, 3)].\n |- Pick two numbers (4, 15) (numbers left: [12, 3]). Try possible operations.\n  |- Try 15 + 4 = 19. Add 19 to the number set. Current number set: [19, 12, 3], target: 20. Options for choosing two numbers: [(19, 12), (19, 3), (12, 3)].\n   |- Pick two numbers (19, 12) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 12 = 31. Add 31 to the number set. Current number set: [31, 3], target: 20, just two numbers left.\n     |- Try 31 + 3 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 31 - 3 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 31 * 3 = 93. Evaluate 93 != 20, drop this branch.\n     |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 19 - 12 = 7. Add 7 to the number set. Current number set: [7, 3], target: 20, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 20, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 20, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 19 * 12 = 228. Add 228 to the number set. Current number set: [228, 3], target: 20, just two numbers left.\n     |- Try 228 + 3 = 231. Evaluate 231 != 20, drop this branch.\n     |- Try 228 - 3 = 225. Evaluate 225 != 20, drop this branch.\n     |- Try 228 * 3 = 684. Evaluate 684 != 20, drop this branch.\n     |- Try 228 \/ 3 = 76. Evaluate 76 != 20, drop this branch.\n    |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [12]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 12], target: 20, just two numbers left.\n     |- Try 22 + 12 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 22 - 12 = 10. Evaluate 10 != 20, drop this branch.\n     |- Try 22 * 12 = 264. Evaluate 264 != 20, drop this branch.\n     |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 12], target: 20, just two numbers left.\n     |- Try 16 + 12 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 16 - 12 = 4. Evaluate 4 != 20, drop this branch.\n     |- Try 16 * 12 = 192. Evaluate 192 != 20, drop this branch.\n     |- Try 16 \/ 12 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 12], target: 20, just two numbers left.\n     |- Try 57 + 12 = 69. Evaluate 69 != 20, drop this branch.\n     |- Try 57 - 12 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 57 * 12 = 684. Evaluate 684 != 20, drop this branch.\n     |- Try 57 \/ 12 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (12, 3) (numbers left: [19]). Try possible operations.\n    |- Try 12 + 3 = 15. Add 15 to the number set. Current number set: [15, 19], target: 20, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 20, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 20, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 12 - 3 = 9. Add 9 to the number set. Current number set: [9, 19], target: 20, just two numbers left.\n     |- Try 19 + 9 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 19 - 9 = 10. Evaluate 10 != 20, drop this branch.\n     |- Try 19 * 9 = 171. Evaluate 171 != 20, drop this branch.\n     |- Try 19 \/ 9 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 12 * 3 = 36. Add 36 to the number set. Current number set: [36, 19], target: 20, just two numbers left.\n     |- Try 36 + 19 = 55. Evaluate 55 != 20, drop this branch.\n     |- Try 36 - 19 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 36 * 19 = 684. Evaluate 684 != 20, drop this branch.\n     |- Try 36 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 12 \/ 3 = 4. Add 4 to the number set. Current number set: [4, 19], target: 20, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 != 20, drop this branch.\n     |- Try 19 - 4 = 15. Evaluate 15 != 20, drop this branch.\n     |- Try 19 * 4 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 19 \/ 4 = 4.8. 4.8 is a decimal, drop this branch.\n  |- Try 15 - 4 = 11. Add 11 to the number set. Current number set: [11, 12, 3], target: 20. Options for choosing two numbers: [(11, 12), (11, 3), (12, 3)].\n   |- Pick two numbers (11, 12) (numbers left: [3]). Try possible operations.\n    |- Try 12 + 11 = 23. Add 23 to the number set. Current number set: [23, 3], target: 20, just two numbers left.\n     |- Try 23 + 3 = 26. Evaluate 26 != 20, drop this branch.\n     |- Try 23 - 3 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 - 3 = 20\nThe step before: 12 + 11 = 23\nThe first step: 15 - 4 = 11\n\nOutput the solution in the required format:\n<Solution>\n15 - 4 = 11\n12 + 11 = 23\n23 - 3 = 20\n<\/Solution>\n","item":{"nums":[4,15,12,3],"solution":["15 - 4 = 11","12 + 11 = 23","23 - 3 = 20"],"target":20}}
+{"instance_id":"countdown_2k_121","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 36, 5, 3]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [4, 36, 5, 3], target: 25. Options for choosing two numbers: [(4, 36), (4, 5), (4, 3), (36, 5), (36, 3), (5, 3)].\n |- Pick two numbers (4, 36) (numbers left: [5, 3]). Try possible operations.\n  |- Try 36 + 4 = 40. Add 40 to the number set. Current number set: [40, 5, 3], target: 25. Options for choosing two numbers: [(40, 5), (40, 3), (5, 3)].\n   |- Pick two numbers (40, 5) (numbers left: [3]). Try possible operations.\n    |- Try 40 + 5 = 45. Add 45 to the number set. Current number set: [45, 3], target: 25, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 25, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 25, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 25, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 25, drop this branch.\n    |- Try 40 - 5 = 35. Add 35 to the number set. Current number set: [35, 3], target: 25, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 != 25, drop this branch.\n     |- Try 35 - 3 = 32. Evaluate 32 != 25, drop this branch.\n     |- Try 35 * 3 = 105. Evaluate 105 != 25, drop this branch.\n     |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 40 * 5 = 200. Add 200 to the number set. Current number set: [200, 3], target: 25, just two numbers left.\n     |- Try 200 + 3 = 203. Evaluate 203 != 25, drop this branch.\n     |- Try 200 - 3 = 197. Evaluate 197 != 25, drop this branch.\n     |- Try 200 * 3 = 600. Evaluate 600 != 25, drop this branch.\n     |- Try 200 \/ 3 = 66.7. 66.7 is a decimal, drop this branch.\n    |- Try 40 \/ 5 = 8. Add 8 to the number set. Current number set: [8, 3], target: 25, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 25, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (40, 3) (numbers left: [5]). Try possible operations.\n    |- Try 40 + 3 = 43. Add 43 to the number set. Current number set: [43, 5], target: 25, just two numbers left.\n     |- Try 43 + 5 = 48. Evaluate 48 != 25, drop this branch.\n     |- Try 43 - 5 = 38. Evaluate 38 != 25, drop this branch.\n     |- Try 43 * 5 = 215. Evaluate 215 != 25, drop this branch.\n     |- Try 43 \/ 5 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 40 - 3 = 37. Add 37 to the number set. Current number set: [37, 5], target: 25, just two numbers left.\n     |- Try 37 + 5 = 42. Evaluate 42 != 25, drop this branch.\n     |- Try 37 - 5 = 32. Evaluate 32 != 25, drop this branch.\n     |- Try 37 * 5 = 185. Evaluate 185 != 25, drop this branch.\n     |- Try 37 \/ 5 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 40 * 3 = 120. Add 120 to the number set. Current number set: [120, 5], target: 25, just two numbers left.\n     |- Try 120 + 5 = 125. Evaluate 125 != 25, drop this branch.\n     |- Try 120 - 5 = 115. Evaluate 115 != 25, drop this branch.\n     |- Try 120 * 5 = 600. Evaluate 600 != 25, drop this branch.\n     |- Try 120 \/ 5 = 24. Evaluate 24 != 25, drop this branch.\n    |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n   |- Pick two numbers (5, 3) (numbers left: [40]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 40], target: 25, just two numbers left.\n     |- Try 40 + 8 = 48. Evaluate 48 != 25, drop this branch.\n     |- Try 40 - 8 = 32. Evaluate 32 != 25, drop this branch.\n     |- Try 40 * 8 = 320. Evaluate 320 != 25, drop this branch.\n     |- Try 40 \/ 8 = 5. Evaluate 5 != 25, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 40], target: 25, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 25, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 25, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 25, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 25, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 40], target: 25, just two numbers left.\n     |- Try 40 + 15 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 40 - 15 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 - 15 = 25\nThe step before: 5 * 3 = 15\nThe first step: 36 + 4 = 40\n\nOutput the solution in the required format:\n<Solution>\n36 + 4 = 40\n5 * 3 = 15\n40 - 15 = 25\n<\/Solution>\n","item":{"nums":[4,36,5,3],"solution":["36 + 4 = 40","5 * 3 = 15","40 - 15 = 25"],"target":25}}
+{"instance_id":"countdown_2k_122","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 7, 28, 35]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [44, 7, 28, 35], target: 26. Options for choosing two numbers: [(44, 7), (44, 28), (44, 35), (7, 28), (7, 35), (28, 35)].\n |- Pick two numbers (44, 7) (numbers left: [28, 35]). Try possible operations.\n  |- Try 44 + 7 = 51. Add 51 to the number set. Current number set: [51, 28, 35], target: 26. Options for choosing two numbers: [(51, 28), (51, 35), (28, 35)].\n   |- Pick two numbers (51, 28) (numbers left: [35]). Try possible operations.\n    |- Try 51 + 28 = 79. Add 79 to the number set. Current number set: [79, 35], target: 26, just two numbers left.\n     |- Try 79 + 35 = 114. Evaluate 114 != 26, drop this branch.\n     |- Try 79 - 35 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 79 * 35 = 2765. 2765 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 35 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 51 - 28 = 23. Add 23 to the number set. Current number set: [23, 35], target: 26, just two numbers left.\n     |- Try 35 + 23 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 35 - 23 = 12. Evaluate 12 != 26, drop this branch.\n     |- Try 35 * 23 = 805. Evaluate 805 != 26, drop this branch.\n     |- Try 35 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 51 * 28 = 1428. Add 1428 to the number set. Current number set: [1428, 35], target: 26, just two numbers left.\n     |- Try 1428 + 35 = 1463. Evaluate 1463 != 26, drop this branch.\n     |- Try 1428 - 35 = 1393. Evaluate 1393 != 26, drop this branch.\n     |- Try 1428 * 35 = 49980. 49980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1428 \/ 35 = 40.8. 40.8 is a decimal, drop this branch.\n    |- Try 51 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (51, 35) (numbers left: [28]). Try possible operations.\n    |- Try 51 + 35 = 86. Add 86 to the number set. Current number set: [86, 28], target: 26, just two numbers left.\n     |- Try 86 + 28 = 114. Evaluate 114 != 26, drop this branch.\n     |- Try 86 - 28 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 86 * 28 = 2408. 2408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 28 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 51 - 35 = 16. Add 16 to the number set. Current number set: [16, 28], target: 26, just two numbers left.\n     |- Try 28 + 16 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 28 - 16 = 12. Evaluate 12 != 26, drop this branch.\n     |- Try 28 * 16 = 448. Evaluate 448 != 26, drop this branch.\n     |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 51 * 35 = 1785. Add 1785 to the number set. Current number set: [1785, 28], target: 26, just two numbers left.\n     |- Try 1785 + 28 = 1813. Evaluate 1813 != 26, drop this branch.\n     |- Try 1785 - 28 = 1757. Evaluate 1757 != 26, drop this branch.\n     |- Try 1785 * 28 = 49980. 49980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1785 \/ 28 = 63.8. 63.8 is a decimal, drop this branch.\n    |- Try 51 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 35) (numbers left: [51]). Try possible operations.\n    |- Try 35 + 28 = 63. Add 63 to the number set. Current number set: [63, 51], target: 26, just two numbers left.\n     |- Try 63 + 51 = 114. Evaluate 114 != 26, drop this branch.\n     |- Try 63 - 51 = 12. Evaluate 12 != 26, drop this branch.\n     |- Try 63 * 51 = 3213. 3213 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 51 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 - 28 = 7. Add 7 to the number set. Current number set: [7, 51], target: 26, just two numbers left.\n     |- Try 51 + 7 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 51 - 7 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 51 * 7 = 357. Evaluate 357 != 26, drop this branch.\n     |- Try 51 \/ 7 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 35 * 28 = 980. Add 980 to the number set. Current number set: [980, 51], target: 26, just two numbers left.\n     |- Try 980 + 51 = 1031. Evaluate 1031 != 26, drop this branch.\n     |- Try 980 - 51 = 929. Evaluate 929 != 26, drop this branch.\n     |- Try 980 * 51 = 49980. 49980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 980 \/ 51 = 19.2. 19.2 is a decimal, drop this branch.\n    |- Try 35 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 44 - 7 = 37. Add 37 to the number set. Current number set: [37, 28, 35], target: 26. Options for choosing two numbers: [(37, 28), (37, 35), (28, 35)].\n   |- Pick two numbers (37, 28) (numbers left: [35]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 35], target: 26, just two numbers left.\n     |- Try 65 + 35 = 100. Evaluate 100 != 26, drop this branch.\n     |- Try 65 - 35 = 30. Evaluate 30 != 26, drop this branch.\n     |- Try 65 * 35 = 2275. 2275 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 35 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 35], target: 26, just two numbers left.\n     |- Try 35 + 9 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 35 - 9 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 - 9 = 26\nThe step before: 37 - 28 = 9\nThe first step: 44 - 7 = 37\n\nOutput the solution in the required format:\n<Solution>\n44 - 7 = 37\n37 - 28 = 9\n35 - 9 = 26\n<\/Solution>\n","item":{"nums":[44,7,28,35],"solution":["44 - 7 = 37","37 - 28 = 9","35 - 9 = 26"],"target":26}}
+{"instance_id":"countdown_2k_123","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [39, 32, 7, 27]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [39, 32, 7, 27], target: 41. Options for choosing two numbers: [(39, 32), (39, 7), (39, 27), (32, 7), (32, 27), (7, 27)].\n |- Pick two numbers (39, 32) (numbers left: [7, 27]). Try possible operations.\n  |- Try 39 + 32 = 71. Add 71 to the number set. Current number set: [71, 7, 27], target: 41. Options for choosing two numbers: [(71, 7), (71, 27), (7, 27)].\n   |- Pick two numbers (71, 7) (numbers left: [27]). Try possible operations.\n    |- Try 71 + 7 = 78. Add 78 to the number set. Current number set: [78, 27], target: 41, just two numbers left.\n     |- Try 78 + 27 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 78 - 27 = 51. Evaluate 51 != 41, drop this branch.\n     |- Try 78 * 27 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 27 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 71 - 7 = 64. Add 64 to the number set. Current number set: [64, 27], target: 41, just two numbers left.\n     |- Try 64 + 27 = 91. Evaluate 91 != 41, drop this branch.\n     |- Try 64 - 27 = 37. Evaluate 37 != 41, drop this branch.\n     |- Try 64 * 27 = 1728. Evaluate 1728 != 41, drop this branch.\n     |- Try 64 \/ 27 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 71 * 7 = 497. Add 497 to the number set. Current number set: [497, 27], target: 41, just two numbers left.\n     |- Try 497 + 27 = 524. Evaluate 524 != 41, drop this branch.\n     |- Try 497 - 27 = 470. Evaluate 470 != 41, drop this branch.\n     |- Try 497 * 27 = 13419. 13419 exceeds the maximum intermediate result, drop this branch.\n     |- Try 497 \/ 27 = 18.4. 18.4 is a decimal, drop this branch.\n    |- Try 71 \/ 7 = 10.1. 10.1 is a decimal, drop this branch.\n   |- Pick two numbers (71, 27) (numbers left: [7]). Try possible operations.\n    |- Try 71 + 27 = 98. Add 98 to the number set. Current number set: [98, 7], target: 41, just two numbers left.\n     |- Try 98 + 7 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 98 - 7 = 91. Evaluate 91 != 41, drop this branch.\n     |- Try 98 * 7 = 686. Evaluate 686 != 41, drop this branch.\n     |- Try 98 \/ 7 = 14. Evaluate 14 != 41, drop this branch.\n    |- Try 71 - 27 = 44. Add 44 to the number set. Current number set: [44, 7], target: 41, just two numbers left.\n     |- Try 44 + 7 = 51. Evaluate 51 != 41, drop this branch.\n     |- Try 44 - 7 = 37. Evaluate 37 != 41, drop this branch.\n     |- Try 44 * 7 = 308. Evaluate 308 != 41, drop this branch.\n     |- Try 44 \/ 7 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 71 * 27 = 1917. Add 1917 to the number set. Current number set: [1917, 7], target: 41, just two numbers left.\n     |- Try 1917 + 7 = 1924. Evaluate 1924 != 41, drop this branch.\n     |- Try 1917 - 7 = 1910. Evaluate 1910 != 41, drop this branch.\n     |- Try 1917 * 7 = 13419. 13419 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1917 \/ 7 = 273.9. 273.9 is a decimal, drop this branch.\n    |- Try 71 \/ 27 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (7, 27) (numbers left: [71]). Try possible operations.\n    |- Try 27 + 7 = 34. Add 34 to the number set. Current number set: [34, 71], target: 41, just two numbers left.\n     |- Try 71 + 34 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 71 - 34 = 37. Evaluate 37 != 41, drop this branch.\n     |- Try 71 * 34 = 2414. 2414 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 34 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 27 - 7 = 20. Add 20 to the number set. Current number set: [20, 71], target: 41, just two numbers left.\n     |- Try 71 + 20 = 91. Evaluate 91 != 41, drop this branch.\n     |- Try 71 - 20 = 51. Evaluate 51 != 41, drop this branch.\n     |- Try 71 * 20 = 1420. Evaluate 1420 != 41, drop this branch.\n     |- Try 71 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 27 * 7 = 189. Add 189 to the number set. Current number set: [189, 71], target: 41, just two numbers left.\n     |- Try 189 + 71 = 260. Evaluate 260 != 41, drop this branch.\n     |- Try 189 - 71 = 118. Evaluate 118 != 41, drop this branch.\n     |- Try 189 * 71 = 13419. 13419 exceeds the maximum intermediate result, drop this branch.\n     |- Try 189 \/ 71 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 27 \/ 7 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 39 - 32 = 7. Add 7 to the number set. Current number set: [7, 7, 27], target: 41. Options for choosing two numbers: [(7, 7), (7, 27), (7, 27)].\n   |- Pick two numbers (7, 7) (numbers left: [27]). Try possible operations.\n    |- Try 7 + 7 = 14. Add 14 to the number set. Current number set: [14, 27], target: 41, just two numbers left.\n     |- Try 27 + 14 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 14 = 41\nThe step before: 7 + 7 = 14\nThe first step: 39 - 32 = 7\n\nOutput the solution in the required format:\n<Solution>\n39 - 32 = 7\n7 + 7 = 14\n27 + 14 = 41\n<\/Solution>\n","item":{"nums":[39,32,7,27],"solution":["39 - 32 = 7","7 + 7 = 14","27 + 14 = 41"],"target":41}}
+{"instance_id":"countdown_2k_124","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 4, 29, 30]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [46, 4, 29, 30], target: 41. Options for choosing two numbers: [(46, 4), (46, 29), (46, 30), (4, 29), (4, 30), (29, 30)].\n |- Pick two numbers (46, 4) (numbers left: [29, 30]). Try possible operations.\n  |- Try 46 + 4 = 50. Add 50 to the number set. Current number set: [50, 29, 30], target: 41. Options for choosing two numbers: [(50, 29), (50, 30), (29, 30)].\n   |- Pick two numbers (50, 29) (numbers left: [30]). Try possible operations.\n    |- Try 50 + 29 = 79. Add 79 to the number set. Current number set: [79, 30], target: 41, just two numbers left.\n     |- Try 79 + 30 = 109. Evaluate 109 != 41, drop this branch.\n     |- Try 79 - 30 = 49. Evaluate 49 != 41, drop this branch.\n     |- Try 79 * 30 = 2370. 2370 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 50 - 29 = 21. Add 21 to the number set. Current number set: [21, 30], target: 41, just two numbers left.\n     |- Try 30 + 21 = 51. Evaluate 51 != 41, drop this branch.\n     |- Try 30 - 21 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 30 * 21 = 630. Evaluate 630 != 41, drop this branch.\n     |- Try 30 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 50 * 29 = 1450. Add 1450 to the number set. Current number set: [1450, 30], target: 41, just two numbers left.\n     |- Try 1450 + 30 = 1480. Evaluate 1480 != 41, drop this branch.\n     |- Try 1450 - 30 = 1420. Evaluate 1420 != 41, drop this branch.\n     |- Try 1450 * 30 = 43500. 43500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1450 \/ 30 = 48.3. 48.3 is a decimal, drop this branch.\n    |- Try 50 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (50, 30) (numbers left: [29]). Try possible operations.\n    |- Try 50 + 30 = 80. Add 80 to the number set. Current number set: [80, 29], target: 41, just two numbers left.\n     |- Try 80 + 29 = 109. Evaluate 109 != 41, drop this branch.\n     |- Try 80 - 29 = 51. Evaluate 51 != 41, drop this branch.\n     |- Try 80 * 29 = 2320. 2320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 29 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 50 - 30 = 20. Add 20 to the number set. Current number set: [20, 29], target: 41, just two numbers left.\n     |- Try 29 + 20 = 49. Evaluate 49 != 41, drop this branch.\n     |- Try 29 - 20 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 29 * 20 = 580. Evaluate 580 != 41, drop this branch.\n     |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 50 * 30 = 1500. Add 1500 to the number set. Current number set: [1500, 29], target: 41, just two numbers left.\n     |- Try 1500 + 29 = 1529. Evaluate 1529 != 41, drop this branch.\n     |- Try 1500 - 29 = 1471. Evaluate 1471 != 41, drop this branch.\n     |- Try 1500 * 29 = 43500. 43500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1500 \/ 29 = 51.7. 51.7 is a decimal, drop this branch.\n    |- Try 50 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (29, 30) (numbers left: [50]). Try possible operations.\n    |- Try 30 + 29 = 59. Add 59 to the number set. Current number set: [59, 50], target: 41, just two numbers left.\n     |- Try 59 + 50 = 109. Evaluate 109 != 41, drop this branch.\n     |- Try 59 - 50 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 59 * 50 = 2950. 2950 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 50 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 - 29 = 1. Add 1 to the number set. Current number set: [1, 50], target: 41, just two numbers left.\n     |- Try 50 + 1 = 51. Evaluate 51 != 41, drop this branch.\n     |- Try 50 - 1 = 49. Evaluate 49 != 41, drop this branch.\n     |- Try 50 * 1 = 50. Evaluate 50 != 41, drop this branch.\n     |- Try 50 \/ 1 = 50. Evaluate 50 != 41, drop this branch.\n    |- Try 30 * 29 = 870. Add 870 to the number set. Current number set: [870, 50], target: 41, just two numbers left.\n     |- Try 870 + 50 = 920. Evaluate 920 != 41, drop this branch.\n     |- Try 870 - 50 = 820. Evaluate 820 != 41, drop this branch.\n     |- Try 870 * 50 = 43500. 43500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 870 \/ 50 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 46 - 4 = 42. Add 42 to the number set. Current number set: [42, 29, 30], target: 41. Options for choosing two numbers: [(42, 29), (42, 30), (29, 30)].\n   |- Pick two numbers (42, 29) (numbers left: [30]). Try possible operations.\n    |- Try 42 + 29 = 71. Add 71 to the number set. Current number set: [71, 30], target: 41, just two numbers left.\n     |- Try 71 + 30 = 101. Evaluate 101 != 41, drop this branch.\n     |- Try 71 - 30 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 71 - 30 = 41\nThe step before: 42 + 29 = 71\nThe first step: 46 - 4 = 42\n\nOutput the solution in the required format:\n<Solution>\n46 - 4 = 42\n42 + 29 = 71\n71 - 30 = 41\n<\/Solution>\n","item":{"nums":[46,4,29,30],"solution":["46 - 4 = 42","42 + 29 = 71","71 - 30 = 41"],"target":41}}
+{"instance_id":"countdown_2k_125","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 8, 47, 4]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [33, 8, 47, 4], target: 26. Options for choosing two numbers: [(33, 8), (33, 47), (33, 4), (8, 47), (8, 4), (47, 4)].\n |- Pick two numbers (33, 8) (numbers left: [47, 4]). Try possible operations.\n  |- Try 33 + 8 = 41. Add 41 to the number set. Current number set: [41, 47, 4], target: 26. Options for choosing two numbers: [(41, 47), (41, 4), (47, 4)].\n   |- Pick two numbers (41, 47) (numbers left: [4]). Try possible operations.\n    |- Try 47 + 41 = 88. Add 88 to the number set. Current number set: [88, 4], target: 26, just two numbers left.\n     |- Try 88 + 4 = 92. Evaluate 92 != 26, drop this branch.\n     |- Try 88 - 4 = 84. Evaluate 84 != 26, drop this branch.\n     |- Try 88 * 4 = 352. Evaluate 352 != 26, drop this branch.\n     |- Try 88 \/ 4 = 22. Evaluate 22 != 26, drop this branch.\n    |- Try 47 - 41 = 6. Add 6 to the number set. Current number set: [6, 4], target: 26, just two numbers left.\n     |- Try 6 + 4 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 6 - 4 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 6 * 4 = 24. Evaluate 24 != 26, drop this branch.\n     |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 47 * 41 = 1927. Add 1927 to the number set. Current number set: [1927, 4], target: 26, just two numbers left.\n     |- Try 1927 + 4 = 1931. Evaluate 1931 != 26, drop this branch.\n     |- Try 1927 - 4 = 1923. Evaluate 1923 != 26, drop this branch.\n     |- Try 1927 * 4 = 7708. 7708 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1927 \/ 4 = 481.8. 481.8 is a decimal, drop this branch.\n    |- Try 47 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (41, 4) (numbers left: [47]). Try possible operations.\n    |- Try 41 + 4 = 45. Add 45 to the number set. Current number set: [45, 47], target: 26, just two numbers left.\n     |- Try 47 + 45 = 92. Evaluate 92 != 26, drop this branch.\n     |- Try 47 - 45 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 47 * 45 = 2115. 2115 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 45 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 41 - 4 = 37. Add 37 to the number set. Current number set: [37, 47], target: 26, just two numbers left.\n     |- Try 47 + 37 = 84. Evaluate 84 != 26, drop this branch.\n     |- Try 47 - 37 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 47 * 37 = 1739. Evaluate 1739 != 26, drop this branch.\n     |- Try 47 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 * 4 = 164. Add 164 to the number set. Current number set: [164, 47], target: 26, just two numbers left.\n     |- Try 164 + 47 = 211. Evaluate 211 != 26, drop this branch.\n     |- Try 164 - 47 = 117. Evaluate 117 != 26, drop this branch.\n     |- Try 164 * 47 = 7708. 7708 exceeds the maximum intermediate result, drop this branch.\n     |- Try 164 \/ 47 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 41 \/ 4 = 10.2. 10.2 is a decimal, drop this branch.\n   |- Pick two numbers (47, 4) (numbers left: [41]). Try possible operations.\n    |- Try 47 + 4 = 51. Add 51 to the number set. Current number set: [51, 41], target: 26, just two numbers left.\n     |- Try 51 + 41 = 92. Evaluate 92 != 26, drop this branch.\n     |- Try 51 - 41 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 51 * 41 = 2091. 2091 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 - 4 = 43. Add 43 to the number set. Current number set: [43, 41], target: 26, just two numbers left.\n     |- Try 43 + 41 = 84. Evaluate 84 != 26, drop this branch.\n     |- Try 43 - 41 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 43 * 41 = 1763. Evaluate 1763 != 26, drop this branch.\n     |- Try 43 \/ 41 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 47 * 4 = 188. Add 188 to the number set. Current number set: [188, 41], target: 26, just two numbers left.\n     |- Try 188 + 41 = 229. Evaluate 229 != 26, drop this branch.\n     |- Try 188 - 41 = 147. Evaluate 147 != 26, drop this branch.\n     |- Try 188 * 41 = 7708. 7708 exceeds the maximum intermediate result, drop this branch.\n     |- Try 188 \/ 41 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 47 \/ 4 = 11.8. 11.8 is a decimal, drop this branch.\n  |- Try 33 - 8 = 25. Add 25 to the number set. Current number set: [25, 47, 4], target: 26. Options for choosing two numbers: [(25, 47), (25, 4), (47, 4)].\n   |- Pick two numbers (25, 47) (numbers left: [4]). Try possible operations.\n    |- Try 47 + 25 = 72. Add 72 to the number set. Current number set: [72, 4], target: 26, just two numbers left.\n     |- Try 72 + 4 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 72 - 4 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 72 * 4 = 288. Evaluate 288 != 26, drop this branch.\n     |- Try 72 \/ 4 = 18. Evaluate 18 != 26, drop this branch.\n    |- Try 47 - 25 = 22. Add 22 to the number set. Current number set: [22, 4], target: 26, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 + 4 = 26\nThe step before: 47 - 25 = 22\nThe first step: 33 - 8 = 25\n\nOutput the solution in the required format:\n<Solution>\n33 - 8 = 25\n47 - 25 = 22\n22 + 4 = 26\n<\/Solution>\n","item":{"nums":[33,8,47,4],"solution":["33 - 8 = 25","47 - 25 = 22","22 + 4 = 26"],"target":26}}
+{"instance_id":"countdown_2k_126","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 27, 2, 34]\nTarget: 47","reference_output":"# Search Procedure\nInitial number set: [12, 27, 2, 34], target: 47. Options for choosing two numbers: [(12, 27), (12, 2), (12, 34), (27, 2), (27, 34), (2, 34)].\n |- Pick two numbers (12, 27) (numbers left: [2, 34]). Try possible operations.\n  |- Try 27 + 12 = 39. Add 39 to the number set. Current number set: [39, 2, 34], target: 47. Options for choosing two numbers: [(39, 2), (39, 34), (2, 34)].\n   |- Pick two numbers (39, 2) (numbers left: [34]). Try possible operations.\n    |- Try 39 + 2 = 41. Add 41 to the number set. Current number set: [41, 34], target: 47, just two numbers left.\n     |- Try 41 + 34 = 75. Evaluate 75 != 47, drop this branch.\n     |- Try 41 - 34 = 7. Evaluate 7 != 47, drop this branch.\n     |- Try 41 * 34 = 1394. Evaluate 1394 != 47, drop this branch.\n     |- Try 41 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 2 = 37. Add 37 to the number set. Current number set: [37, 34], target: 47, just two numbers left.\n     |- Try 37 + 34 = 71. Evaluate 71 != 47, drop this branch.\n     |- Try 37 - 34 = 3. Evaluate 3 != 47, drop this branch.\n     |- Try 37 * 34 = 1258. Evaluate 1258 != 47, drop this branch.\n     |- Try 37 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 39 * 2 = 78. Add 78 to the number set. Current number set: [78, 34], target: 47, just two numbers left.\n     |- Try 78 + 34 = 112. Evaluate 112 != 47, drop this branch.\n     |- Try 78 - 34 = 44. Evaluate 44 != 47, drop this branch.\n     |- Try 78 * 34 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 34 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n   |- Pick two numbers (39, 34) (numbers left: [2]). Try possible operations.\n    |- Try 39 + 34 = 73. Add 73 to the number set. Current number set: [73, 2], target: 47, just two numbers left.\n     |- Try 73 + 2 = 75. Evaluate 75 != 47, drop this branch.\n     |- Try 73 - 2 = 71. Evaluate 71 != 47, drop this branch.\n     |- Try 73 * 2 = 146. Evaluate 146 != 47, drop this branch.\n     |- Try 73 \/ 2 = 36.5. 36.5 is a decimal, drop this branch.\n    |- Try 39 - 34 = 5. Add 5 to the number set. Current number set: [5, 2], target: 47, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 47, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 47, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 47, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 39 * 34 = 1326. Add 1326 to the number set. Current number set: [1326, 2], target: 47, just two numbers left.\n     |- Try 1326 + 2 = 1328. Evaluate 1328 != 47, drop this branch.\n     |- Try 1326 - 2 = 1324. Evaluate 1324 != 47, drop this branch.\n     |- Try 1326 * 2 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1326 \/ 2 = 663. Evaluate 663 != 47, drop this branch.\n    |- Try 39 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (2, 34) (numbers left: [39]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 39], target: 47, just two numbers left.\n     |- Try 39 + 36 = 75. Evaluate 75 != 47, drop this branch.\n     |- Try 39 - 36 = 3. Evaluate 3 != 47, drop this branch.\n     |- Try 39 * 36 = 1404. Evaluate 1404 != 47, drop this branch.\n     |- Try 39 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 39], target: 47, just two numbers left.\n     |- Try 39 + 32 = 71. Evaluate 71 != 47, drop this branch.\n     |- Try 39 - 32 = 7. Evaluate 7 != 47, drop this branch.\n     |- Try 39 * 32 = 1248. Evaluate 1248 != 47, drop this branch.\n     |- Try 39 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 39], target: 47, just two numbers left.\n     |- Try 68 + 39 = 107. Evaluate 107 != 47, drop this branch.\n     |- Try 68 - 39 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 68 * 39 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 34 \/ 2 = 17. Add 17 to the number set. Current number set: [17, 39], target: 47, just two numbers left.\n     |- Try 39 + 17 = 56. Evaluate 56 != 47, drop this branch.\n     |- Try 39 - 17 = 22. Evaluate 22 != 47, drop this branch.\n     |- Try 39 * 17 = 663. Evaluate 663 != 47, drop this branch.\n     |- Try 39 \/ 17 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 27 - 12 = 15. Add 15 to the number set. Current number set: [15, 2, 34], target: 47. Options for choosing two numbers: [(15, 2), (15, 34), (2, 34)].\n   |- Pick two numbers (15, 2) (numbers left: [34]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 34], target: 47, just two numbers left.\n     |- Try 34 + 17 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 34 - 17 = 17. Evaluate 17 != 47, drop this branch.\n     |- Try 34 * 17 = 578. Evaluate 578 != 47, drop this branch.\n     |- Try 34 \/ 17 = 2. Evaluate 2 != 47, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 34], target: 47, just two numbers left.\n     |- Try 34 + 13 = 47. Evaluate 47 == 47, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 13 = 47\nThe step before: 15 - 2 = 13\nThe first step: 27 - 12 = 15\n\nOutput the solution in the required format:\n<Solution>\n27 - 12 = 15\n15 - 2 = 13\n34 + 13 = 47\n<\/Solution>\n","item":{"nums":[12,27,2,34],"solution":["27 - 12 = 15","15 - 2 = 13","34 + 13 = 47"],"target":47}}
+{"instance_id":"countdown_2k_127","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [16, 35, 28, 36]\nTarget: 45","reference_output":"# Search Procedure\nInitial number set: [16, 35, 28, 36], target: 45. Options for choosing two numbers: [(16, 35), (16, 28), (16, 36), (35, 28), (35, 36), (28, 36)].\n |- Pick two numbers (16, 35) (numbers left: [28, 36]). Try possible operations.\n  |- Try 35 + 16 = 51. Add 51 to the number set. Current number set: [51, 28, 36], target: 45. Options for choosing two numbers: [(51, 28), (51, 36), (28, 36)].\n   |- Pick two numbers (51, 28) (numbers left: [36]). Try possible operations.\n    |- Try 51 + 28 = 79. Add 79 to the number set. Current number set: [79, 36], target: 45, just two numbers left.\n     |- Try 79 + 36 = 115. Evaluate 115 != 45, drop this branch.\n     |- Try 79 - 36 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 79 * 36 = 2844. 2844 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 36 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 51 - 28 = 23. Add 23 to the number set. Current number set: [23, 36], target: 45, just two numbers left.\n     |- Try 36 + 23 = 59. Evaluate 59 != 45, drop this branch.\n     |- Try 36 - 23 = 13. Evaluate 13 != 45, drop this branch.\n     |- Try 36 * 23 = 828. Evaluate 828 != 45, drop this branch.\n     |- Try 36 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 51 * 28 = 1428. Add 1428 to the number set. Current number set: [1428, 36], target: 45, just two numbers left.\n     |- Try 1428 + 36 = 1464. Evaluate 1464 != 45, drop this branch.\n     |- Try 1428 - 36 = 1392. Evaluate 1392 != 45, drop this branch.\n     |- Try 1428 * 36 = 51408. 51408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1428 \/ 36 = 39.7. 39.7 is a decimal, drop this branch.\n    |- Try 51 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (51, 36) (numbers left: [28]). Try possible operations.\n    |- Try 51 + 36 = 87. Add 87 to the number set. Current number set: [87, 28], target: 45, just two numbers left.\n     |- Try 87 + 28 = 115. Evaluate 115 != 45, drop this branch.\n     |- Try 87 - 28 = 59. Evaluate 59 != 45, drop this branch.\n     |- Try 87 * 28 = 2436. 2436 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 28 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 51 - 36 = 15. Add 15 to the number set. Current number set: [15, 28], target: 45, just two numbers left.\n     |- Try 28 + 15 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 28 - 15 = 13. Evaluate 13 != 45, drop this branch.\n     |- Try 28 * 15 = 420. Evaluate 420 != 45, drop this branch.\n     |- Try 28 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 51 * 36 = 1836. Add 1836 to the number set. Current number set: [1836, 28], target: 45, just two numbers left.\n     |- Try 1836 + 28 = 1864. Evaluate 1864 != 45, drop this branch.\n     |- Try 1836 - 28 = 1808. Evaluate 1808 != 45, drop this branch.\n     |- Try 1836 * 28 = 51408. 51408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1836 \/ 28 = 65.6. 65.6 is a decimal, drop this branch.\n    |- Try 51 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 36) (numbers left: [51]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 51], target: 45, just two numbers left.\n     |- Try 64 + 51 = 115. Evaluate 115 != 45, drop this branch.\n     |- Try 64 - 51 = 13. Evaluate 13 != 45, drop this branch.\n     |- Try 64 * 51 = 3264. 3264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 51 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 51], target: 45, just two numbers left.\n     |- Try 51 + 8 = 59. Evaluate 59 != 45, drop this branch.\n     |- Try 51 - 8 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 51 * 8 = 408. Evaluate 408 != 45, drop this branch.\n     |- Try 51 \/ 8 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 51], target: 45, just two numbers left.\n     |- Try 1008 + 51 = 1059. Evaluate 1059 != 45, drop this branch.\n     |- Try 1008 - 51 = 957. Evaluate 957 != 45, drop this branch.\n     |- Try 1008 * 51 = 51408. 51408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 51 = 19.8. 19.8 is a decimal, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 35 - 16 = 19. Add 19 to the number set. Current number set: [19, 28, 36], target: 45. Options for choosing two numbers: [(19, 28), (19, 36), (28, 36)].\n   |- Pick two numbers (19, 28) (numbers left: [36]). Try possible operations.\n    |- Try 28 + 19 = 47. Add 47 to the number set. Current number set: [47, 36], target: 45, just two numbers left.\n     |- Try 47 + 36 = 83. Evaluate 83 != 45, drop this branch.\n     |- Try 47 - 36 = 11. Evaluate 11 != 45, drop this branch.\n     |- Try 47 * 36 = 1692. Evaluate 1692 != 45, drop this branch.\n     |- Try 47 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 28 - 19 = 9. Add 9 to the number set. Current number set: [9, 36], target: 45, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 == 45, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 + 9 = 45\nThe step before: 28 - 19 = 9\nThe first step: 35 - 16 = 19\n\nOutput the solution in the required format:\n<Solution>\n35 - 16 = 19\n28 - 19 = 9\n36 + 9 = 45\n<\/Solution>\n","item":{"nums":[16,35,28,36],"solution":["35 - 16 = 19","28 - 19 = 9","36 + 9 = 45"],"target":45}}
+{"instance_id":"countdown_2k_128","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 46, 29, 18]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [49, 46, 29, 18], target: 44. Options for choosing two numbers: [(49, 46), (49, 29), (49, 18), (46, 29), (46, 18), (29, 18)].\n |- Pick two numbers (49, 46) (numbers left: [29, 18]). Try possible operations.\n  |- Try 49 + 46 = 95. Add 95 to the number set. Current number set: [95, 29, 18], target: 44. Options for choosing two numbers: [(95, 29), (95, 18), (29, 18)].\n   |- Pick two numbers (95, 29) (numbers left: [18]). Try possible operations.\n    |- Try 95 + 29 = 124. Add 124 to the number set. Current number set: [124, 18], target: 44, just two numbers left.\n     |- Try 124 + 18 = 142. Evaluate 142 != 44, drop this branch.\n     |- Try 124 - 18 = 106. Evaluate 106 != 44, drop this branch.\n     |- Try 124 * 18 = 2232. 2232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 18 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 95 - 29 = 66. Add 66 to the number set. Current number set: [66, 18], target: 44, just two numbers left.\n     |- Try 66 + 18 = 84. Evaluate 84 != 44, drop this branch.\n     |- Try 66 - 18 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 66 * 18 = 1188. Evaluate 1188 != 44, drop this branch.\n     |- Try 66 \/ 18 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 95 * 29 = 2755. 2755 exceeds the maximum intermediate result, drop this branch.\n    |- Try 95 \/ 29 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (95, 18) (numbers left: [29]). Try possible operations.\n    |- Try 95 + 18 = 113. Add 113 to the number set. Current number set: [113, 29], target: 44, just two numbers left.\n     |- Try 113 + 29 = 142. Evaluate 142 != 44, drop this branch.\n     |- Try 113 - 29 = 84. Evaluate 84 != 44, drop this branch.\n     |- Try 113 * 29 = 3277. 3277 exceeds the maximum intermediate result, drop this branch.\n     |- Try 113 \/ 29 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 95 - 18 = 77. Add 77 to the number set. Current number set: [77, 29], target: 44, just two numbers left.\n     |- Try 77 + 29 = 106. Evaluate 106 != 44, drop this branch.\n     |- Try 77 - 29 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 77 * 29 = 2233. 2233 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 29 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 95 * 18 = 1710. Add 1710 to the number set. Current number set: [1710, 29], target: 44, just two numbers left.\n     |- Try 1710 + 29 = 1739. Evaluate 1739 != 44, drop this branch.\n     |- Try 1710 - 29 = 1681. Evaluate 1681 != 44, drop this branch.\n     |- Try 1710 * 29 = 49590. 49590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 \/ 29 = 59.0. 59.0 is a decimal, drop this branch.\n    |- Try 95 \/ 18 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (29, 18) (numbers left: [95]). Try possible operations.\n    |- Try 29 + 18 = 47. Add 47 to the number set. Current number set: [47, 95], target: 44, just two numbers left.\n     |- Try 95 + 47 = 142. Evaluate 142 != 44, drop this branch.\n     |- Try 95 - 47 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 95 * 47 = 4465. 4465 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 47 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 29 - 18 = 11. Add 11 to the number set. Current number set: [11, 95], target: 44, just two numbers left.\n     |- Try 95 + 11 = 106. Evaluate 106 != 44, drop this branch.\n     |- Try 95 - 11 = 84. Evaluate 84 != 44, drop this branch.\n     |- Try 95 * 11 = 1045. Evaluate 1045 != 44, drop this branch.\n     |- Try 95 \/ 11 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 29 * 18 = 522. Add 522 to the number set. Current number set: [522, 95], target: 44, just two numbers left.\n     |- Try 522 + 95 = 617. Evaluate 617 != 44, drop this branch.\n     |- Try 522 - 95 = 427. Evaluate 427 != 44, drop this branch.\n     |- Try 522 * 95 = 49590. 49590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 522 \/ 95 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 29 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 49 - 46 = 3. Add 3 to the number set. Current number set: [3, 29, 18], target: 44. Options for choosing two numbers: [(3, 29), (3, 18), (29, 18)].\n   |- Pick two numbers (3, 29) (numbers left: [18]). Try possible operations.\n    |- Try 29 + 3 = 32. Add 32 to the number set. Current number set: [32, 18], target: 44, just two numbers left.\n     |- Try 32 + 18 = 50. Evaluate 50 != 44, drop this branch.\n     |- Try 32 - 18 = 14. Evaluate 14 != 44, drop this branch.\n     |- Try 32 * 18 = 576. Evaluate 576 != 44, drop this branch.\n     |- Try 32 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 29 - 3 = 26. Add 26 to the number set. Current number set: [26, 18], target: 44, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 + 18 = 44\nThe step before: 29 - 3 = 26\nThe first step: 49 - 46 = 3\n\nOutput the solution in the required format:\n<Solution>\n49 - 46 = 3\n29 - 3 = 26\n26 + 18 = 44\n<\/Solution>\n","item":{"nums":[49,46,29,18],"solution":["49 - 46 = 3","29 - 3 = 26","26 + 18 = 44"],"target":44}}
+{"instance_id":"countdown_2k_129","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 39, 22, 2]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [30, 39, 22, 2], target: 25. Options for choosing two numbers: [(30, 39), (30, 22), (30, 2), (39, 22), (39, 2), (22, 2)].\n |- Pick two numbers (30, 39) (numbers left: [22, 2]). Try possible operations.\n  |- Try 39 + 30 = 69. Add 69 to the number set. Current number set: [69, 22, 2], target: 25. Options for choosing two numbers: [(69, 22), (69, 2), (22, 2)].\n   |- Pick two numbers (69, 22) (numbers left: [2]). Try possible operations.\n    |- Try 69 + 22 = 91. Add 91 to the number set. Current number set: [91, 2], target: 25, just two numbers left.\n     |- Try 91 + 2 = 93. Evaluate 93 != 25, drop this branch.\n     |- Try 91 - 2 = 89. Evaluate 89 != 25, drop this branch.\n     |- Try 91 * 2 = 182. Evaluate 182 != 25, drop this branch.\n     |- Try 91 \/ 2 = 45.5. 45.5 is a decimal, drop this branch.\n    |- Try 69 - 22 = 47. Add 47 to the number set. Current number set: [47, 2], target: 25, just two numbers left.\n     |- Try 47 + 2 = 49. Evaluate 49 != 25, drop this branch.\n     |- Try 47 - 2 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 47 * 2 = 94. Evaluate 94 != 25, drop this branch.\n     |- Try 47 \/ 2 = 23.5. 23.5 is a decimal, drop this branch.\n    |- Try 69 * 22 = 1518. Add 1518 to the number set. Current number set: [1518, 2], target: 25, just two numbers left.\n     |- Try 1518 + 2 = 1520. Evaluate 1520 != 25, drop this branch.\n     |- Try 1518 - 2 = 1516. Evaluate 1516 != 25, drop this branch.\n     |- Try 1518 * 2 = 3036. 3036 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 \/ 2 = 759. Evaluate 759 != 25, drop this branch.\n    |- Try 69 \/ 22 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (69, 2) (numbers left: [22]). Try possible operations.\n    |- Try 69 + 2 = 71. Add 71 to the number set. Current number set: [71, 22], target: 25, just two numbers left.\n     |- Try 71 + 22 = 93. Evaluate 93 != 25, drop this branch.\n     |- Try 71 - 22 = 49. Evaluate 49 != 25, drop this branch.\n     |- Try 71 * 22 = 1562. Evaluate 1562 != 25, drop this branch.\n     |- Try 71 \/ 22 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 69 - 2 = 67. Add 67 to the number set. Current number set: [67, 22], target: 25, just two numbers left.\n     |- Try 67 + 22 = 89. Evaluate 89 != 25, drop this branch.\n     |- Try 67 - 22 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 67 * 22 = 1474. Evaluate 1474 != 25, drop this branch.\n     |- Try 67 \/ 22 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 69 * 2 = 138. Add 138 to the number set. Current number set: [138, 22], target: 25, just two numbers left.\n     |- Try 138 + 22 = 160. Evaluate 160 != 25, drop this branch.\n     |- Try 138 - 22 = 116. Evaluate 116 != 25, drop this branch.\n     |- Try 138 * 22 = 3036. 3036 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 22 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 69 \/ 2 = 34.5. 34.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 2) (numbers left: [69]). Try possible operations.\n    |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 69], target: 25, just two numbers left.\n     |- Try 69 + 24 = 93. Evaluate 93 != 25, drop this branch.\n     |- Try 69 - 24 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 69 * 24 = 1656. Evaluate 1656 != 25, drop this branch.\n     |- Try 69 \/ 24 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 69], target: 25, just two numbers left.\n     |- Try 69 + 20 = 89. Evaluate 89 != 25, drop this branch.\n     |- Try 69 - 20 = 49. Evaluate 49 != 25, drop this branch.\n     |- Try 69 * 20 = 1380. Evaluate 1380 != 25, drop this branch.\n     |- Try 69 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 69], target: 25, just two numbers left.\n     |- Try 69 + 44 = 113. Evaluate 113 != 25, drop this branch.\n     |- Try 69 - 44 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 69 - 44 = 25\nThe step before: 22 * 2 = 44\nThe first step: 39 + 30 = 69\n\nOutput the solution in the required format:\n<Solution>\n39 + 30 = 69\n22 * 2 = 44\n69 - 44 = 25\n<\/Solution>\n","item":{"nums":[30,39,22,2],"solution":["39 + 30 = 69","22 * 2 = 44","69 - 44 = 25"],"target":25}}
+{"instance_id":"countdown_2k_130","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 25, 26, 7]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [19, 25, 26, 7], target: 13. Options for choosing two numbers: [(19, 25), (19, 26), (19, 7), (25, 26), (25, 7), (26, 7)].\n |- Pick two numbers (19, 25) (numbers left: [26, 7]). Try possible operations.\n  |- Try 25 + 19 = 44. Add 44 to the number set. Current number set: [44, 26, 7], target: 13. Options for choosing two numbers: [(44, 26), (44, 7), (26, 7)].\n   |- Pick two numbers (44, 26) (numbers left: [7]). Try possible operations.\n    |- Try 44 + 26 = 70. Add 70 to the number set. Current number set: [70, 7], target: 13, just two numbers left.\n     |- Try 70 + 7 = 77. Evaluate 77 != 13, drop this branch.\n     |- Try 70 - 7 = 63. Evaluate 63 != 13, drop this branch.\n     |- Try 70 * 7 = 490. Evaluate 490 != 13, drop this branch.\n     |- Try 70 \/ 7 = 10. Evaluate 10 != 13, drop this branch.\n    |- Try 44 - 26 = 18. Add 18 to the number set. Current number set: [18, 7], target: 13, just two numbers left.\n     |- Try 18 + 7 = 25. Evaluate 25 != 13, drop this branch.\n     |- Try 18 - 7 = 11. Evaluate 11 != 13, drop this branch.\n     |- Try 18 * 7 = 126. Evaluate 126 != 13, drop this branch.\n     |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 44 * 26 = 1144. Add 1144 to the number set. Current number set: [1144, 7], target: 13, just two numbers left.\n     |- Try 1144 + 7 = 1151. Evaluate 1151 != 13, drop this branch.\n     |- Try 1144 - 7 = 1137. Evaluate 1137 != 13, drop this branch.\n     |- Try 1144 * 7 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1144 \/ 7 = 163.4. 163.4 is a decimal, drop this branch.\n    |- Try 44 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (44, 7) (numbers left: [26]). Try possible operations.\n    |- Try 44 + 7 = 51. Add 51 to the number set. Current number set: [51, 26], target: 13, just two numbers left.\n     |- Try 51 + 26 = 77. Evaluate 77 != 13, drop this branch.\n     |- Try 51 - 26 = 25. Evaluate 25 != 13, drop this branch.\n     |- Try 51 * 26 = 1326. Evaluate 1326 != 13, drop this branch.\n     |- Try 51 \/ 26 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 44 - 7 = 37. Add 37 to the number set. Current number set: [37, 26], target: 13, just two numbers left.\n     |- Try 37 + 26 = 63. Evaluate 63 != 13, drop this branch.\n     |- Try 37 - 26 = 11. Evaluate 11 != 13, drop this branch.\n     |- Try 37 * 26 = 962. Evaluate 962 != 13, drop this branch.\n     |- Try 37 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 7 = 308. Add 308 to the number set. Current number set: [308, 26], target: 13, just two numbers left.\n     |- Try 308 + 26 = 334. Evaluate 334 != 13, drop this branch.\n     |- Try 308 - 26 = 282. Evaluate 282 != 13, drop this branch.\n     |- Try 308 * 26 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 308 \/ 26 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 44 \/ 7 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (26, 7) (numbers left: [44]). Try possible operations.\n    |- Try 26 + 7 = 33. Add 33 to the number set. Current number set: [33, 44], target: 13, just two numbers left.\n     |- Try 44 + 33 = 77. Evaluate 77 != 13, drop this branch.\n     |- Try 44 - 33 = 11. Evaluate 11 != 13, drop this branch.\n     |- Try 44 * 33 = 1452. Evaluate 1452 != 13, drop this branch.\n     |- Try 44 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 - 7 = 19. Add 19 to the number set. Current number set: [19, 44], target: 13, just two numbers left.\n     |- Try 44 + 19 = 63. Evaluate 63 != 13, drop this branch.\n     |- Try 44 - 19 = 25. Evaluate 25 != 13, drop this branch.\n     |- Try 44 * 19 = 836. Evaluate 836 != 13, drop this branch.\n     |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 26 * 7 = 182. Add 182 to the number set. Current number set: [182, 44], target: 13, just two numbers left.\n     |- Try 182 + 44 = 226. Evaluate 226 != 13, drop this branch.\n     |- Try 182 - 44 = 138. Evaluate 138 != 13, drop this branch.\n     |- Try 182 * 44 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 182 \/ 44 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 25 - 19 = 6. Add 6 to the number set. Current number set: [6, 26, 7], target: 13. Options for choosing two numbers: [(6, 26), (6, 7), (26, 7)].\n   |- Pick two numbers (6, 26) (numbers left: [7]). Try possible operations.\n    |- Try 26 + 6 = 32. Add 32 to the number set. Current number set: [32, 7], target: 13, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 13, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 13, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 13, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 26 - 6 = 20. Add 20 to the number set. Current number set: [20, 7], target: 13, just two numbers left.\n     |- Try 20 + 7 = 27. Evaluate 27 != 13, drop this branch.\n     |- Try 20 - 7 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 - 7 = 13\nThe step before: 26 - 6 = 20\nThe first step: 25 - 19 = 6\n\nOutput the solution in the required format:\n<Solution>\n25 - 19 = 6\n26 - 6 = 20\n20 - 7 = 13\n<\/Solution>\n","item":{"nums":[19,25,26,7],"solution":["25 - 19 = 6","26 - 6 = 20","20 - 7 = 13"],"target":13}}
+{"instance_id":"countdown_2k_131","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 33, 17, 23]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [41, 33, 17, 23], target: 14. Options for choosing two numbers: [(41, 33), (41, 17), (41, 23), (33, 17), (33, 23), (17, 23)].\n |- Pick two numbers (41, 33) (numbers left: [17, 23]). Try possible operations.\n  |- Try 41 + 33 = 74. Add 74 to the number set. Current number set: [74, 17, 23], target: 14. Options for choosing two numbers: [(74, 17), (74, 23), (17, 23)].\n   |- Pick two numbers (74, 17) (numbers left: [23]). Try possible operations.\n    |- Try 74 + 17 = 91. Add 91 to the number set. Current number set: [91, 23], target: 14, just two numbers left.\n     |- Try 91 + 23 = 114. Evaluate 114 != 14, drop this branch.\n     |- Try 91 - 23 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 91 * 23 = 2093. 2093 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 23 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 74 - 17 = 57. Add 57 to the number set. Current number set: [57, 23], target: 14, just two numbers left.\n     |- Try 57 + 23 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 57 - 23 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 57 * 23 = 1311. Evaluate 1311 != 14, drop this branch.\n     |- Try 57 \/ 23 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 74 * 17 = 1258. Add 1258 to the number set. Current number set: [1258, 23], target: 14, just two numbers left.\n     |- Try 1258 + 23 = 1281. Evaluate 1281 != 14, drop this branch.\n     |- Try 1258 - 23 = 1235. Evaluate 1235 != 14, drop this branch.\n     |- Try 1258 * 23 = 28934. 28934 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1258 \/ 23 = 54.7. 54.7 is a decimal, drop this branch.\n    |- Try 74 \/ 17 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (74, 23) (numbers left: [17]). Try possible operations.\n    |- Try 74 + 23 = 97. Add 97 to the number set. Current number set: [97, 17], target: 14, just two numbers left.\n     |- Try 97 + 17 = 114. Evaluate 114 != 14, drop this branch.\n     |- Try 97 - 17 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 97 * 17 = 1649. Evaluate 1649 != 14, drop this branch.\n     |- Try 97 \/ 17 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 74 - 23 = 51. Add 51 to the number set. Current number set: [51, 17], target: 14, just two numbers left.\n     |- Try 51 + 17 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 51 - 17 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 51 * 17 = 867. Evaluate 867 != 14, drop this branch.\n     |- Try 51 \/ 17 = 3. Evaluate 3 != 14, drop this branch.\n    |- Try 74 * 23 = 1702. Add 1702 to the number set. Current number set: [1702, 17], target: 14, just two numbers left.\n     |- Try 1702 + 17 = 1719. Evaluate 1719 != 14, drop this branch.\n     |- Try 1702 - 17 = 1685. Evaluate 1685 != 14, drop this branch.\n     |- Try 1702 * 17 = 28934. 28934 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1702 \/ 17 = 100.1. 100.1 is a decimal, drop this branch.\n    |- Try 74 \/ 23 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (17, 23) (numbers left: [74]). Try possible operations.\n    |- Try 23 + 17 = 40. Add 40 to the number set. Current number set: [40, 74], target: 14, just two numbers left.\n     |- Try 74 + 40 = 114. Evaluate 114 != 14, drop this branch.\n     |- Try 74 - 40 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 74 * 40 = 2960. 2960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 40 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 23 - 17 = 6. Add 6 to the number set. Current number set: [6, 74], target: 14, just two numbers left.\n     |- Try 74 + 6 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 74 - 6 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 74 * 6 = 444. Evaluate 444 != 14, drop this branch.\n     |- Try 74 \/ 6 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 23 * 17 = 391. Add 391 to the number set. Current number set: [391, 74], target: 14, just two numbers left.\n     |- Try 391 + 74 = 465. Evaluate 465 != 14, drop this branch.\n     |- Try 391 - 74 = 317. Evaluate 317 != 14, drop this branch.\n     |- Try 391 * 74 = 28934. 28934 exceeds the maximum intermediate result, drop this branch.\n     |- Try 391 \/ 74 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 23 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 41 - 33 = 8. Add 8 to the number set. Current number set: [8, 17, 23], target: 14. Options for choosing two numbers: [(8, 17), (8, 23), (17, 23)].\n   |- Pick two numbers (8, 17) (numbers left: [23]). Try possible operations.\n    |- Try 17 + 8 = 25. Add 25 to the number set. Current number set: [25, 23], target: 14, just two numbers left.\n     |- Try 25 + 23 = 48. Evaluate 48 != 14, drop this branch.\n     |- Try 25 - 23 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 25 * 23 = 575. Evaluate 575 != 14, drop this branch.\n     |- Try 25 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 17 - 8 = 9. Add 9 to the number set. Current number set: [9, 23], target: 14, just two numbers left.\n     |- Try 23 + 9 = 32. Evaluate 32 != 14, drop this branch.\n     |- Try 23 - 9 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 - 9 = 14\nThe step before: 17 - 8 = 9\nThe first step: 41 - 33 = 8\n\nOutput the solution in the required format:\n<Solution>\n41 - 33 = 8\n17 - 8 = 9\n23 - 9 = 14\n<\/Solution>\n","item":{"nums":[41,33,17,23],"solution":["41 - 33 = 8","17 - 8 = 9","23 - 9 = 14"],"target":14}}
+{"instance_id":"countdown_2k_132","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [11, 21, 27, 26]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [11, 21, 27, 26], target: 11. Options for choosing two numbers: [(11, 21), (11, 27), (11, 26), (21, 27), (21, 26), (27, 26)].\n |- Pick two numbers (11, 21) (numbers left: [27, 26]). Try possible operations.\n  |- Try 21 + 11 = 32. Add 32 to the number set. Current number set: [32, 27, 26], target: 11. Options for choosing two numbers: [(32, 27), (32, 26), (27, 26)].\n   |- Pick two numbers (32, 27) (numbers left: [26]). Try possible operations.\n    |- Try 32 + 27 = 59. Add 59 to the number set. Current number set: [59, 26], target: 11, just two numbers left.\n     |- Try 59 + 26 = 85. Evaluate 85 != 11, drop this branch.\n     |- Try 59 - 26 = 33. Evaluate 33 != 11, drop this branch.\n     |- Try 59 * 26 = 1534. Evaluate 1534 != 11, drop this branch.\n     |- Try 59 \/ 26 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 - 27 = 5. Add 5 to the number set. Current number set: [5, 26], target: 11, just two numbers left.\n     |- Try 26 + 5 = 31. Evaluate 31 != 11, drop this branch.\n     |- Try 26 - 5 = 21. Evaluate 21 != 11, drop this branch.\n     |- Try 26 * 5 = 130. Evaluate 130 != 11, drop this branch.\n     |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 32 * 27 = 864. Add 864 to the number set. Current number set: [864, 26], target: 11, just two numbers left.\n     |- Try 864 + 26 = 890. Evaluate 890 != 11, drop this branch.\n     |- Try 864 - 26 = 838. Evaluate 838 != 11, drop this branch.\n     |- Try 864 * 26 = 22464. 22464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 26 = 33.2. 33.2 is a decimal, drop this branch.\n    |- Try 32 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (32, 26) (numbers left: [27]). Try possible operations.\n    |- Try 32 + 26 = 58. Add 58 to the number set. Current number set: [58, 27], target: 11, just two numbers left.\n     |- Try 58 + 27 = 85. Evaluate 85 != 11, drop this branch.\n     |- Try 58 - 27 = 31. Evaluate 31 != 11, drop this branch.\n     |- Try 58 * 27 = 1566. Evaluate 1566 != 11, drop this branch.\n     |- Try 58 \/ 27 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 32 - 26 = 6. Add 6 to the number set. Current number set: [6, 27], target: 11, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 11, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 11, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 32 * 26 = 832. Add 832 to the number set. Current number set: [832, 27], target: 11, just two numbers left.\n     |- Try 832 + 27 = 859. Evaluate 859 != 11, drop this branch.\n     |- Try 832 - 27 = 805. Evaluate 805 != 11, drop this branch.\n     |- Try 832 * 27 = 22464. 22464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 832 \/ 27 = 30.8. 30.8 is a decimal, drop this branch.\n    |- Try 32 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (27, 26) (numbers left: [32]). Try possible operations.\n    |- Try 27 + 26 = 53. Add 53 to the number set. Current number set: [53, 32], target: 11, just two numbers left.\n     |- Try 53 + 32 = 85. Evaluate 85 != 11, drop this branch.\n     |- Try 53 - 32 = 21. Evaluate 21 != 11, drop this branch.\n     |- Try 53 * 32 = 1696. Evaluate 1696 != 11, drop this branch.\n     |- Try 53 \/ 32 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 27 - 26 = 1. Add 1 to the number set. Current number set: [1, 32], target: 11, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 11, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 11, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 11, drop this branch.\n    |- Try 27 * 26 = 702. Add 702 to the number set. Current number set: [702, 32], target: 11, just two numbers left.\n     |- Try 702 + 32 = 734. Evaluate 734 != 11, drop this branch.\n     |- Try 702 - 32 = 670. Evaluate 670 != 11, drop this branch.\n     |- Try 702 * 32 = 22464. 22464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 702 \/ 32 = 21.9. 21.9 is a decimal, drop this branch.\n    |- Try 27 \/ 26 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 21 - 11 = 10. Add 10 to the number set. Current number set: [10, 27, 26], target: 11. Options for choosing two numbers: [(10, 27), (10, 26), (27, 26)].\n   |- Pick two numbers (10, 27) (numbers left: [26]). Try possible operations.\n    |- Try 27 + 10 = 37. Add 37 to the number set. Current number set: [37, 26], target: 11, just two numbers left.\n     |- Try 37 + 26 = 63. Evaluate 63 != 11, drop this branch.\n     |- Try 37 - 26 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 37 - 26 = 11\nThe step before: 27 + 10 = 37\nThe first step: 21 - 11 = 10\n\nOutput the solution in the required format:\n<Solution>\n21 - 11 = 10\n27 + 10 = 37\n37 - 26 = 11\n<\/Solution>\n","item":{"nums":[11,21,27,26],"solution":["21 - 11 = 10","27 + 10 = 37","37 - 26 = 11"],"target":11}}
+{"instance_id":"countdown_2k_133","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [14, 33, 3, 30]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [14, 33, 3, 30], target: 46. Options for choosing two numbers: [(14, 33), (14, 3), (14, 30), (33, 3), (33, 30), (3, 30)].\n |- Pick two numbers (14, 33) (numbers left: [3, 30]). Try possible operations.\n  |- Try 33 + 14 = 47. Add 47 to the number set. Current number set: [47, 3, 30], target: 46. Options for choosing two numbers: [(47, 3), (47, 30), (3, 30)].\n   |- Pick two numbers (47, 3) (numbers left: [30]). Try possible operations.\n    |- Try 47 + 3 = 50. Add 50 to the number set. Current number set: [50, 30], target: 46, just two numbers left.\n     |- Try 50 + 30 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 50 - 30 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 50 * 30 = 1500. Evaluate 1500 != 46, drop this branch.\n     |- Try 50 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 47 - 3 = 44. Add 44 to the number set. Current number set: [44, 30], target: 46, just two numbers left.\n     |- Try 44 + 30 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 44 - 30 = 14. Evaluate 14 != 46, drop this branch.\n     |- Try 44 * 30 = 1320. Evaluate 1320 != 46, drop this branch.\n     |- Try 44 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 47 * 3 = 141. Add 141 to the number set. Current number set: [141, 30], target: 46, just two numbers left.\n     |- Try 141 + 30 = 171. Evaluate 171 != 46, drop this branch.\n     |- Try 141 - 30 = 111. Evaluate 111 != 46, drop this branch.\n     |- Try 141 * 30 = 4230. 4230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 141 \/ 30 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n   |- Pick two numbers (47, 30) (numbers left: [3]). Try possible operations.\n    |- Try 47 + 30 = 77. Add 77 to the number set. Current number set: [77, 3], target: 46, just two numbers left.\n     |- Try 77 + 3 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 77 - 3 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 77 * 3 = 231. Evaluate 231 != 46, drop this branch.\n     |- Try 77 \/ 3 = 25.7. 25.7 is a decimal, drop this branch.\n    |- Try 47 - 30 = 17. Add 17 to the number set. Current number set: [17, 3], target: 46, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 46, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 46, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 47 * 30 = 1410. Add 1410 to the number set. Current number set: [1410, 3], target: 46, just two numbers left.\n     |- Try 1410 + 3 = 1413. Evaluate 1413 != 46, drop this branch.\n     |- Try 1410 - 3 = 1407. Evaluate 1407 != 46, drop this branch.\n     |- Try 1410 * 3 = 4230. 4230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1410 \/ 3 = 470. Evaluate 470 != 46, drop this branch.\n    |- Try 47 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (3, 30) (numbers left: [47]). Try possible operations.\n    |- Try 30 + 3 = 33. Add 33 to the number set. Current number set: [33, 47], target: 46, just two numbers left.\n     |- Try 47 + 33 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 47 - 33 = 14. Evaluate 14 != 46, drop this branch.\n     |- Try 47 * 33 = 1551. Evaluate 1551 != 46, drop this branch.\n     |- Try 47 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 - 3 = 27. Add 27 to the number set. Current number set: [27, 47], target: 46, just two numbers left.\n     |- Try 47 + 27 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 47 - 27 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 47 * 27 = 1269. Evaluate 1269 != 46, drop this branch.\n     |- Try 47 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 30 * 3 = 90. Add 90 to the number set. Current number set: [90, 47], target: 46, just two numbers left.\n     |- Try 90 + 47 = 137. Evaluate 137 != 46, drop this branch.\n     |- Try 90 - 47 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 90 * 47 = 4230. 4230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 47 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 \/ 3 = 10. Add 10 to the number set. Current number set: [10, 47], target: 46, just two numbers left.\n     |- Try 47 + 10 = 57. Evaluate 57 != 46, drop this branch.\n     |- Try 47 - 10 = 37. Evaluate 37 != 46, drop this branch.\n     |- Try 47 * 10 = 470. Evaluate 470 != 46, drop this branch.\n     |- Try 47 \/ 10 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 33 - 14 = 19. Add 19 to the number set. Current number set: [19, 3, 30], target: 46. Options for choosing two numbers: [(19, 3), (19, 30), (3, 30)].\n   |- Pick two numbers (19, 3) (numbers left: [30]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 30], target: 46, just two numbers left.\n     |- Try 30 + 22 = 52. Evaluate 52 != 46, drop this branch.\n     |- Try 30 - 22 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 30 * 22 = 660. Evaluate 660 != 46, drop this branch.\n     |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 30], target: 46, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 + 16 = 46\nThe step before: 19 - 3 = 16\nThe first step: 33 - 14 = 19\n\nOutput the solution in the required format:\n<Solution>\n33 - 14 = 19\n19 - 3 = 16\n30 + 16 = 46\n<\/Solution>\n","item":{"nums":[14,33,3,30],"solution":["33 - 14 = 19","19 - 3 = 16","30 + 16 = 46"],"target":46}}
+{"instance_id":"countdown_2k_134","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 26, 11, 5]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [48, 26, 11, 5], target: 16. Options for choosing two numbers: [(48, 26), (48, 11), (48, 5), (26, 11), (26, 5), (11, 5)].\n |- Pick two numbers (48, 26) (numbers left: [11, 5]). Try possible operations.\n  |- Try 48 + 26 = 74. Add 74 to the number set. Current number set: [74, 11, 5], target: 16. Options for choosing two numbers: [(74, 11), (74, 5), (11, 5)].\n   |- Pick two numbers (74, 11) (numbers left: [5]). Try possible operations.\n    |- Try 74 + 11 = 85. Add 85 to the number set. Current number set: [85, 5], target: 16, just two numbers left.\n     |- Try 85 + 5 = 90. Evaluate 90 != 16, drop this branch.\n     |- Try 85 - 5 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 85 * 5 = 425. Evaluate 425 != 16, drop this branch.\n     |- Try 85 \/ 5 = 17. Evaluate 17 != 16, drop this branch.\n    |- Try 74 - 11 = 63. Add 63 to the number set. Current number set: [63, 5], target: 16, just two numbers left.\n     |- Try 63 + 5 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 63 - 5 = 58. Evaluate 58 != 16, drop this branch.\n     |- Try 63 * 5 = 315. Evaluate 315 != 16, drop this branch.\n     |- Try 63 \/ 5 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 74 * 11 = 814. Add 814 to the number set. Current number set: [814, 5], target: 16, just two numbers left.\n     |- Try 814 + 5 = 819. Evaluate 819 != 16, drop this branch.\n     |- Try 814 - 5 = 809. Evaluate 809 != 16, drop this branch.\n     |- Try 814 * 5 = 4070. 4070 exceeds the maximum intermediate result, drop this branch.\n     |- Try 814 \/ 5 = 162.8. 162.8 is a decimal, drop this branch.\n    |- Try 74 \/ 11 = 6.7. 6.7 is a decimal, drop this branch.\n   |- Pick two numbers (74, 5) (numbers left: [11]). Try possible operations.\n    |- Try 74 + 5 = 79. Add 79 to the number set. Current number set: [79, 11], target: 16, just two numbers left.\n     |- Try 79 + 11 = 90. Evaluate 90 != 16, drop this branch.\n     |- Try 79 - 11 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 79 * 11 = 869. Evaluate 869 != 16, drop this branch.\n     |- Try 79 \/ 11 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 74 - 5 = 69. Add 69 to the number set. Current number set: [69, 11], target: 16, just two numbers left.\n     |- Try 69 + 11 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 69 - 11 = 58. Evaluate 58 != 16, drop this branch.\n     |- Try 69 * 11 = 759. Evaluate 759 != 16, drop this branch.\n     |- Try 69 \/ 11 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 74 * 5 = 370. Add 370 to the number set. Current number set: [370, 11], target: 16, just two numbers left.\n     |- Try 370 + 11 = 381. Evaluate 381 != 16, drop this branch.\n     |- Try 370 - 11 = 359. Evaluate 359 != 16, drop this branch.\n     |- Try 370 * 11 = 4070. 4070 exceeds the maximum intermediate result, drop this branch.\n     |- Try 370 \/ 11 = 33.6. 33.6 is a decimal, drop this branch.\n    |- Try 74 \/ 5 = 14.8. 14.8 is a decimal, drop this branch.\n   |- Pick two numbers (11, 5) (numbers left: [74]). Try possible operations.\n    |- Try 11 + 5 = 16. Add 16 to the number set. Current number set: [16, 74], target: 16, just two numbers left.\n     |- Try 74 + 16 = 90. Evaluate 90 != 16, drop this branch.\n     |- Try 74 - 16 = 58. Evaluate 58 != 16, drop this branch.\n     |- Try 74 * 16 = 1184. Evaluate 1184 != 16, drop this branch.\n     |- Try 74 \/ 16 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 11 - 5 = 6. Add 6 to the number set. Current number set: [6, 74], target: 16, just two numbers left.\n     |- Try 74 + 6 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 74 - 6 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 74 * 6 = 444. Evaluate 444 != 16, drop this branch.\n     |- Try 74 \/ 6 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 11 * 5 = 55. Add 55 to the number set. Current number set: [55, 74], target: 16, just two numbers left.\n     |- Try 74 + 55 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 74 - 55 = 19. Evaluate 19 != 16, drop this branch.\n     |- Try 74 * 55 = 4070. 4070 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 55 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 11 \/ 5 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 48 - 26 = 22. Add 22 to the number set. Current number set: [22, 11, 5], target: 16. Options for choosing two numbers: [(22, 11), (22, 5), (11, 5)].\n   |- Pick two numbers (22, 11) (numbers left: [5]). Try possible operations.\n    |- Try 22 + 11 = 33. Add 33 to the number set. Current number set: [33, 5], target: 16, just two numbers left.\n     |- Try 33 + 5 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 33 - 5 = 28. Evaluate 28 != 16, drop this branch.\n     |- Try 33 * 5 = 165. Evaluate 165 != 16, drop this branch.\n     |- Try 33 \/ 5 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 22 - 11 = 11. Add 11 to the number set. Current number set: [11, 5], target: 16, just two numbers left.\n     |- Try 11 + 5 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 11 + 5 = 16\nThe step before: 22 - 11 = 11\nThe first step: 48 - 26 = 22\n\nOutput the solution in the required format:\n<Solution>\n48 - 26 = 22\n22 - 11 = 11\n11 + 5 = 16\n<\/Solution>\n","item":{"nums":[48,26,11,5],"solution":["48 - 26 = 22","22 - 11 = 11","11 + 5 = 16"],"target":16}}
+{"instance_id":"countdown_2k_135","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 43, 11, 47]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [7, 43, 11, 47], target: 22. Options for choosing two numbers: [(7, 43), (7, 11), (7, 47), (43, 11), (43, 47), (11, 47)].\n |- Pick two numbers (7, 43) (numbers left: [11, 47]). Try possible operations.\n  |- Try 43 + 7 = 50. Add 50 to the number set. Current number set: [50, 11, 47], target: 22. Options for choosing two numbers: [(50, 11), (50, 47), (11, 47)].\n   |- Pick two numbers (50, 11) (numbers left: [47]). Try possible operations.\n    |- Try 50 + 11 = 61. Add 61 to the number set. Current number set: [61, 47], target: 22, just two numbers left.\n     |- Try 61 + 47 = 108. Evaluate 108 != 22, drop this branch.\n     |- Try 61 - 47 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 61 * 47 = 2867. 2867 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 47 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 50 - 11 = 39. Add 39 to the number set. Current number set: [39, 47], target: 22, just two numbers left.\n     |- Try 47 + 39 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 47 - 39 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 47 * 39 = 1833. Evaluate 1833 != 22, drop this branch.\n     |- Try 47 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 50 * 11 = 550. Add 550 to the number set. Current number set: [550, 47], target: 22, just two numbers left.\n     |- Try 550 + 47 = 597. Evaluate 597 != 22, drop this branch.\n     |- Try 550 - 47 = 503. Evaluate 503 != 22, drop this branch.\n     |- Try 550 * 47 = 25850. 25850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 550 \/ 47 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 50 \/ 11 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (50, 47) (numbers left: [11]). Try possible operations.\n    |- Try 50 + 47 = 97. Add 97 to the number set. Current number set: [97, 11], target: 22, just two numbers left.\n     |- Try 97 + 11 = 108. Evaluate 108 != 22, drop this branch.\n     |- Try 97 - 11 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 97 * 11 = 1067. Evaluate 1067 != 22, drop this branch.\n     |- Try 97 \/ 11 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 50 - 47 = 3. Add 3 to the number set. Current number set: [3, 11], target: 22, just two numbers left.\n     |- Try 11 + 3 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 11 - 3 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 11 * 3 = 33. Evaluate 33 != 22, drop this branch.\n     |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 50 * 47 = 2350. 2350 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (11, 47) (numbers left: [50]). Try possible operations.\n    |- Try 47 + 11 = 58. Add 58 to the number set. Current number set: [58, 50], target: 22, just two numbers left.\n     |- Try 58 + 50 = 108. Evaluate 108 != 22, drop this branch.\n     |- Try 58 - 50 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 58 * 50 = 2900. 2900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 50 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 - 11 = 36. Add 36 to the number set. Current number set: [36, 50], target: 22, just two numbers left.\n     |- Try 50 + 36 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 50 - 36 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 50 * 36 = 1800. Evaluate 1800 != 22, drop this branch.\n     |- Try 50 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 47 * 11 = 517. Add 517 to the number set. Current number set: [517, 50], target: 22, just two numbers left.\n     |- Try 517 + 50 = 567. Evaluate 567 != 22, drop this branch.\n     |- Try 517 - 50 = 467. Evaluate 467 != 22, drop this branch.\n     |- Try 517 * 50 = 25850. 25850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 517 \/ 50 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 47 \/ 11 = 4.3. 4.3 is a decimal, drop this branch.\n  |- Try 43 - 7 = 36. Add 36 to the number set. Current number set: [36, 11, 47], target: 22. Options for choosing two numbers: [(36, 11), (36, 47), (11, 47)].\n   |- Pick two numbers (36, 11) (numbers left: [47]). Try possible operations.\n    |- Try 36 + 11 = 47. Add 47 to the number set. Current number set: [47, 47], target: 22, just two numbers left.\n     |- Try 47 + 47 = 94. Evaluate 94 != 22, drop this branch.\n     |- Try 47 - 47 = 0. Evaluate 0 != 22, drop this branch.\n     |- Try 47 * 47 = 2209. 2209 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 47 = 1. Evaluate 1 != 22, drop this branch.\n    |- Try 36 - 11 = 25. Add 25 to the number set. Current number set: [25, 47], target: 22, just two numbers left.\n     |- Try 47 + 25 = 72. Evaluate 72 != 22, drop this branch.\n     |- Try 47 - 25 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 - 25 = 22\nThe step before: 36 - 11 = 25\nThe first step: 43 - 7 = 36\n\nOutput the solution in the required format:\n<Solution>\n43 - 7 = 36\n36 - 11 = 25\n47 - 25 = 22\n<\/Solution>\n","item":{"nums":[7,43,11,47],"solution":["43 - 7 = 36","36 - 11 = 25","47 - 25 = 22"],"target":22}}
+{"instance_id":"countdown_2k_136","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 22, 22, 16]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [47, 22, 22, 16], target: 48. Options for choosing two numbers: [(47, 22), (47, 22), (47, 16), (22, 22), (22, 16), (22, 16)].\n |- Pick two numbers (47, 22) (numbers left: [22, 16]). Try possible operations.\n  |- Try 47 + 22 = 69. Add 69 to the number set. Current number set: [69, 22, 16], target: 48. Options for choosing two numbers: [(69, 22), (69, 16), (22, 16)].\n   |- Pick two numbers (69, 22) (numbers left: [16]). Try possible operations.\n    |- Try 69 + 22 = 91. Add 91 to the number set. Current number set: [91, 16], target: 48, just two numbers left.\n     |- Try 91 + 16 = 107. Evaluate 107 != 48, drop this branch.\n     |- Try 91 - 16 = 75. Evaluate 75 != 48, drop this branch.\n     |- Try 91 * 16 = 1456. Evaluate 1456 != 48, drop this branch.\n     |- Try 91 \/ 16 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 69 - 22 = 47. Add 47 to the number set. Current number set: [47, 16], target: 48, just two numbers left.\n     |- Try 47 + 16 = 63. Evaluate 63 != 48, drop this branch.\n     |- Try 47 - 16 = 31. Evaluate 31 != 48, drop this branch.\n     |- Try 47 * 16 = 752. Evaluate 752 != 48, drop this branch.\n     |- Try 47 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 69 * 22 = 1518. Add 1518 to the number set. Current number set: [1518, 16], target: 48, just two numbers left.\n     |- Try 1518 + 16 = 1534. Evaluate 1534 != 48, drop this branch.\n     |- Try 1518 - 16 = 1502. Evaluate 1502 != 48, drop this branch.\n     |- Try 1518 * 16 = 24288. 24288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 \/ 16 = 94.9. 94.9 is a decimal, drop this branch.\n    |- Try 69 \/ 22 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (69, 16) (numbers left: [22]). Try possible operations.\n    |- Try 69 + 16 = 85. Add 85 to the number set. Current number set: [85, 22], target: 48, just two numbers left.\n     |- Try 85 + 22 = 107. Evaluate 107 != 48, drop this branch.\n     |- Try 85 - 22 = 63. Evaluate 63 != 48, drop this branch.\n     |- Try 85 * 22 = 1870. Evaluate 1870 != 48, drop this branch.\n     |- Try 85 \/ 22 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 69 - 16 = 53. Add 53 to the number set. Current number set: [53, 22], target: 48, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 48, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 48, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 48, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 69 * 16 = 1104. Add 1104 to the number set. Current number set: [1104, 22], target: 48, just two numbers left.\n     |- Try 1104 + 22 = 1126. Evaluate 1126 != 48, drop this branch.\n     |- Try 1104 - 22 = 1082. Evaluate 1082 != 48, drop this branch.\n     |- Try 1104 * 22 = 24288. 24288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1104 \/ 22 = 50.2. 50.2 is a decimal, drop this branch.\n    |- Try 69 \/ 16 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 16) (numbers left: [69]). Try possible operations.\n    |- Try 22 + 16 = 38. Add 38 to the number set. Current number set: [38, 69], target: 48, just two numbers left.\n     |- Try 69 + 38 = 107. Evaluate 107 != 48, drop this branch.\n     |- Try 69 - 38 = 31. Evaluate 31 != 48, drop this branch.\n     |- Try 69 * 38 = 2622. 2622 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 38 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 22 - 16 = 6. Add 6 to the number set. Current number set: [6, 69], target: 48, just two numbers left.\n     |- Try 69 + 6 = 75. Evaluate 75 != 48, drop this branch.\n     |- Try 69 - 6 = 63. Evaluate 63 != 48, drop this branch.\n     |- Try 69 * 6 = 414. Evaluate 414 != 48, drop this branch.\n     |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 22 * 16 = 352. Add 352 to the number set. Current number set: [352, 69], target: 48, just two numbers left.\n     |- Try 352 + 69 = 421. Evaluate 421 != 48, drop this branch.\n     |- Try 352 - 69 = 283. Evaluate 283 != 48, drop this branch.\n     |- Try 352 * 69 = 24288. 24288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 69 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 47 - 22 = 25. Add 25 to the number set. Current number set: [25, 22, 16], target: 48. Options for choosing two numbers: [(25, 22), (25, 16), (22, 16)].\n   |- Pick two numbers (25, 22) (numbers left: [16]). Try possible operations.\n    |- Try 25 + 22 = 47. Add 47 to the number set. Current number set: [47, 16], target: 48, just two numbers left.\n     |- Try 47 + 16 = 63. Evaluate 63 != 48, drop this branch.\n     |- Try 47 - 16 = 31. Evaluate 31 != 48, drop this branch.\n     |- Try 47 * 16 = 752. Evaluate 752 != 48, drop this branch.\n     |- Try 47 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 25 - 22 = 3. Add 3 to the number set. Current number set: [3, 16], target: 48, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 48, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 * 3 = 48\nThe step before: 25 - 22 = 3\nThe first step: 47 - 22 = 25\n\nOutput the solution in the required format:\n<Solution>\n47 - 22 = 25\n25 - 22 = 3\n16 * 3 = 48\n<\/Solution>\n","item":{"nums":[47,22,22,16],"solution":["47 - 22 = 25","25 - 22 = 3","16 * 3 = 48"],"target":48}}
+{"instance_id":"countdown_2k_137","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 5, 22, 9]\nTarget: 39","reference_output":"# Search Procedure\nInitial number set: [31, 5, 22, 9], target: 39. Options for choosing two numbers: [(31, 5), (31, 22), (31, 9), (5, 22), (5, 9), (22, 9)].\n |- Pick two numbers (31, 5) (numbers left: [22, 9]). Try possible operations.\n  |- Try 31 + 5 = 36. Add 36 to the number set. Current number set: [36, 22, 9], target: 39. Options for choosing two numbers: [(36, 22), (36, 9), (22, 9)].\n   |- Pick two numbers (36, 22) (numbers left: [9]). Try possible operations.\n    |- Try 36 + 22 = 58. Add 58 to the number set. Current number set: [58, 9], target: 39, just two numbers left.\n     |- Try 58 + 9 = 67. Evaluate 67 != 39, drop this branch.\n     |- Try 58 - 9 = 49. Evaluate 49 != 39, drop this branch.\n     |- Try 58 * 9 = 522. Evaluate 522 != 39, drop this branch.\n     |- Try 58 \/ 9 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 36 - 22 = 14. Add 14 to the number set. Current number set: [14, 9], target: 39, just two numbers left.\n     |- Try 14 + 9 = 23. Evaluate 23 != 39, drop this branch.\n     |- Try 14 - 9 = 5. Evaluate 5 != 39, drop this branch.\n     |- Try 14 * 9 = 126. Evaluate 126 != 39, drop this branch.\n     |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 * 22 = 792. Add 792 to the number set. Current number set: [792, 9], target: 39, just two numbers left.\n     |- Try 792 + 9 = 801. Evaluate 801 != 39, drop this branch.\n     |- Try 792 - 9 = 783. Evaluate 783 != 39, drop this branch.\n     |- Try 792 * 9 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 9 = 88. Evaluate 88 != 39, drop this branch.\n    |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 9) (numbers left: [22]). Try possible operations.\n    |- Try 36 + 9 = 45. Add 45 to the number set. Current number set: [45, 22], target: 39, just two numbers left.\n     |- Try 45 + 22 = 67. Evaluate 67 != 39, drop this branch.\n     |- Try 45 - 22 = 23. Evaluate 23 != 39, drop this branch.\n     |- Try 45 * 22 = 990. Evaluate 990 != 39, drop this branch.\n     |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 36 - 9 = 27. Add 27 to the number set. Current number set: [27, 22], target: 39, just two numbers left.\n     |- Try 27 + 22 = 49. Evaluate 49 != 39, drop this branch.\n     |- Try 27 - 22 = 5. Evaluate 5 != 39, drop this branch.\n     |- Try 27 * 22 = 594. Evaluate 594 != 39, drop this branch.\n     |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 9 = 324. Add 324 to the number set. Current number set: [324, 22], target: 39, just two numbers left.\n     |- Try 324 + 22 = 346. Evaluate 346 != 39, drop this branch.\n     |- Try 324 - 22 = 302. Evaluate 302 != 39, drop this branch.\n     |- Try 324 * 22 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 22 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 36 \/ 9 = 4. Add 4 to the number set. Current number set: [4, 22], target: 39, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 39, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 39, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 39, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 9) (numbers left: [36]). Try possible operations.\n    |- Try 22 + 9 = 31. Add 31 to the number set. Current number set: [31, 36], target: 39, just two numbers left.\n     |- Try 36 + 31 = 67. Evaluate 67 != 39, drop this branch.\n     |- Try 36 - 31 = 5. Evaluate 5 != 39, drop this branch.\n     |- Try 36 * 31 = 1116. Evaluate 1116 != 39, drop this branch.\n     |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 9 = 13. Add 13 to the number set. Current number set: [13, 36], target: 39, just two numbers left.\n     |- Try 36 + 13 = 49. Evaluate 49 != 39, drop this branch.\n     |- Try 36 - 13 = 23. Evaluate 23 != 39, drop this branch.\n     |- Try 36 * 13 = 468. Evaluate 468 != 39, drop this branch.\n     |- Try 36 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 22 * 9 = 198. Add 198 to the number set. Current number set: [198, 36], target: 39, just two numbers left.\n     |- Try 198 + 36 = 234. Evaluate 234 != 39, drop this branch.\n     |- Try 198 - 36 = 162. Evaluate 162 != 39, drop this branch.\n     |- Try 198 * 36 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 36 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 22 \/ 9 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 31 - 5 = 26. Add 26 to the number set. Current number set: [26, 22, 9], target: 39. Options for choosing two numbers: [(26, 22), (26, 9), (22, 9)].\n   |- Pick two numbers (26, 22) (numbers left: [9]). Try possible operations.\n    |- Try 26 + 22 = 48. Add 48 to the number set. Current number set: [48, 9], target: 39, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 39, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 == 39, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 9 = 39\nThe step before: 26 + 22 = 48\nThe first step: 31 - 5 = 26\n\nOutput the solution in the required format:\n<Solution>\n31 - 5 = 26\n26 + 22 = 48\n48 - 9 = 39\n<\/Solution>\n","item":{"nums":[31,5,22,9],"solution":["31 - 5 = 26","26 + 22 = 48","48 - 9 = 39"],"target":39}}
+{"instance_id":"countdown_2k_138","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 47, 23, 33]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [49, 47, 23, 33], target: 12. Options for choosing two numbers: [(49, 47), (49, 23), (49, 33), (47, 23), (47, 33), (23, 33)].\n |- Pick two numbers (49, 47) (numbers left: [23, 33]). Try possible operations.\n  |- Try 49 + 47 = 96. Add 96 to the number set. Current number set: [96, 23, 33], target: 12. Options for choosing two numbers: [(96, 23), (96, 33), (23, 33)].\n   |- Pick two numbers (96, 23) (numbers left: [33]). Try possible operations.\n    |- Try 96 + 23 = 119. Add 119 to the number set. Current number set: [119, 33], target: 12, just two numbers left.\n     |- Try 119 + 33 = 152. Evaluate 152 != 12, drop this branch.\n     |- Try 119 - 33 = 86. Evaluate 86 != 12, drop this branch.\n     |- Try 119 * 33 = 3927. 3927 exceeds the maximum intermediate result, drop this branch.\n     |- Try 119 \/ 33 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 96 - 23 = 73. Add 73 to the number set. Current number set: [73, 33], target: 12, just two numbers left.\n     |- Try 73 + 33 = 106. Evaluate 106 != 12, drop this branch.\n     |- Try 73 - 33 = 40. Evaluate 40 != 12, drop this branch.\n     |- Try 73 * 33 = 2409. 2409 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 96 * 23 = 2208. 2208 exceeds the maximum intermediate result, drop this branch.\n    |- Try 96 \/ 23 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (96, 33) (numbers left: [23]). Try possible operations.\n    |- Try 96 + 33 = 129. Add 129 to the number set. Current number set: [129, 23], target: 12, just two numbers left.\n     |- Try 129 + 23 = 152. Evaluate 152 != 12, drop this branch.\n     |- Try 129 - 23 = 106. Evaluate 106 != 12, drop this branch.\n     |- Try 129 * 23 = 2967. 2967 exceeds the maximum intermediate result, drop this branch.\n     |- Try 129 \/ 23 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 96 - 33 = 63. Add 63 to the number set. Current number set: [63, 23], target: 12, just two numbers left.\n     |- Try 63 + 23 = 86. Evaluate 86 != 12, drop this branch.\n     |- Try 63 - 23 = 40. Evaluate 40 != 12, drop this branch.\n     |- Try 63 * 23 = 1449. Evaluate 1449 != 12, drop this branch.\n     |- Try 63 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 96 * 33 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n    |- Try 96 \/ 33 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (23, 33) (numbers left: [96]). Try possible operations.\n    |- Try 33 + 23 = 56. Add 56 to the number set. Current number set: [56, 96], target: 12, just two numbers left.\n     |- Try 96 + 56 = 152. Evaluate 152 != 12, drop this branch.\n     |- Try 96 - 56 = 40. Evaluate 40 != 12, drop this branch.\n     |- Try 96 * 56 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 56 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 33 - 23 = 10. Add 10 to the number set. Current number set: [10, 96], target: 12, just two numbers left.\n     |- Try 96 + 10 = 106. Evaluate 106 != 12, drop this branch.\n     |- Try 96 - 10 = 86. Evaluate 86 != 12, drop this branch.\n     |- Try 96 * 10 = 960. Evaluate 960 != 12, drop this branch.\n     |- Try 96 \/ 10 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 33 * 23 = 759. Add 759 to the number set. Current number set: [759, 96], target: 12, just two numbers left.\n     |- Try 759 + 96 = 855. Evaluate 855 != 12, drop this branch.\n     |- Try 759 - 96 = 663. Evaluate 663 != 12, drop this branch.\n     |- Try 759 * 96 = 72864. 72864 exceeds the maximum intermediate result, drop this branch.\n     |- Try 759 \/ 96 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 33 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 49 - 47 = 2. Add 2 to the number set. Current number set: [2, 23, 33], target: 12. Options for choosing two numbers: [(2, 23), (2, 33), (23, 33)].\n   |- Pick two numbers (2, 23) (numbers left: [33]). Try possible operations.\n    |- Try 23 + 2 = 25. Add 25 to the number set. Current number set: [25, 33], target: 12, just two numbers left.\n     |- Try 33 + 25 = 58. Evaluate 58 != 12, drop this branch.\n     |- Try 33 - 25 = 8. Evaluate 8 != 12, drop this branch.\n     |- Try 33 * 25 = 825. Evaluate 825 != 12, drop this branch.\n     |- Try 33 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 23 - 2 = 21. Add 21 to the number set. Current number set: [21, 33], target: 12, just two numbers left.\n     |- Try 33 + 21 = 54. Evaluate 54 != 12, drop this branch.\n     |- Try 33 - 21 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 - 21 = 12\nThe step before: 23 - 2 = 21\nThe first step: 49 - 47 = 2\n\nOutput the solution in the required format:\n<Solution>\n49 - 47 = 2\n23 - 2 = 21\n33 - 21 = 12\n<\/Solution>\n","item":{"nums":[49,47,23,33],"solution":["49 - 47 = 2","23 - 2 = 21","33 - 21 = 12"],"target":12}}
+{"instance_id":"countdown_2k_139","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 41, 11, 6]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [7, 41, 11, 6], target: 18. Options for choosing two numbers: [(7, 41), (7, 11), (7, 6), (41, 11), (41, 6), (11, 6)].\n |- Pick two numbers (7, 41) (numbers left: [11, 6]). Try possible operations.\n  |- Try 41 + 7 = 48. Add 48 to the number set. Current number set: [48, 11, 6], target: 18. Options for choosing two numbers: [(48, 11), (48, 6), (11, 6)].\n   |- Pick two numbers (48, 11) (numbers left: [6]). Try possible operations.\n    |- Try 48 + 11 = 59. Add 59 to the number set. Current number set: [59, 6], target: 18, just two numbers left.\n     |- Try 59 + 6 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 59 - 6 = 53. Evaluate 53 != 18, drop this branch.\n     |- Try 59 * 6 = 354. Evaluate 354 != 18, drop this branch.\n     |- Try 59 \/ 6 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 48 - 11 = 37. Add 37 to the number set. Current number set: [37, 6], target: 18, just two numbers left.\n     |- Try 37 + 6 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 37 - 6 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 37 * 6 = 222. Evaluate 222 != 18, drop this branch.\n     |- Try 37 \/ 6 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 48 * 11 = 528. Add 528 to the number set. Current number set: [528, 6], target: 18, just two numbers left.\n     |- Try 528 + 6 = 534. Evaluate 534 != 18, drop this branch.\n     |- Try 528 - 6 = 522. Evaluate 522 != 18, drop this branch.\n     |- Try 528 * 6 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 6 = 88. Evaluate 88 != 18, drop this branch.\n    |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (48, 6) (numbers left: [11]). Try possible operations.\n    |- Try 48 + 6 = 54. Add 54 to the number set. Current number set: [54, 11], target: 18, just two numbers left.\n     |- Try 54 + 11 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 54 - 11 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 54 * 11 = 594. Evaluate 594 != 18, drop this branch.\n     |- Try 54 \/ 11 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 48 - 6 = 42. Add 42 to the number set. Current number set: [42, 11], target: 18, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 18, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 42 * 11 = 462. Evaluate 462 != 18, drop this branch.\n     |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 * 6 = 288. Add 288 to the number set. Current number set: [288, 11], target: 18, just two numbers left.\n     |- Try 288 + 11 = 299. Evaluate 299 != 18, drop this branch.\n     |- Try 288 - 11 = 277. Evaluate 277 != 18, drop this branch.\n     |- Try 288 * 11 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 11 = 26.2. 26.2 is a decimal, drop this branch.\n    |- Try 48 \/ 6 = 8. Add 8 to the number set. Current number set: [8, 11], target: 18, just two numbers left.\n     |- Try 11 + 8 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 11 - 8 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 11 * 8 = 88. Evaluate 88 != 18, drop this branch.\n     |- Try 11 \/ 8 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (11, 6) (numbers left: [48]). Try possible operations.\n    |- Try 11 + 6 = 17. Add 17 to the number set. Current number set: [17, 48], target: 18, just two numbers left.\n     |- Try 48 + 17 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 48 - 17 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 48 * 17 = 816. Evaluate 816 != 18, drop this branch.\n     |- Try 48 \/ 17 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 11 - 6 = 5. Add 5 to the number set. Current number set: [5, 48], target: 18, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 18, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 18, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 11 * 6 = 66. Add 66 to the number set. Current number set: [66, 48], target: 18, just two numbers left.\n     |- Try 66 + 48 = 114. Evaluate 114 != 18, drop this branch.\n     |- Try 66 - 48 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 66 - 48 = 18\nThe step before: 11 * 6 = 66\nThe first step: 41 + 7 = 48\n\nOutput the solution in the required format:\n<Solution>\n41 + 7 = 48\n11 * 6 = 66\n66 - 48 = 18\n<\/Solution>\n","item":{"nums":[7,41,11,6],"solution":["41 + 7 = 48","11 * 6 = 66","66 - 48 = 18"],"target":18}}
+{"instance_id":"countdown_2k_140","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 14, 34, 1]\nTarget: 40","reference_output":"# Search Procedure\nInitial number set: [7, 14, 34, 1], target: 40. Options for choosing two numbers: [(7, 14), (7, 34), (7, 1), (14, 34), (14, 1), (34, 1)].\n |- Pick two numbers (7, 14) (numbers left: [34, 1]). Try possible operations.\n  |- Try 14 + 7 = 21. Add 21 to the number set. Current number set: [21, 34, 1], target: 40. Options for choosing two numbers: [(21, 34), (21, 1), (34, 1)].\n   |- Pick two numbers (21, 34) (numbers left: [1]). Try possible operations.\n    |- Try 34 + 21 = 55. Add 55 to the number set. Current number set: [55, 1], target: 40, just two numbers left.\n     |- Try 55 + 1 = 56. Evaluate 56 != 40, drop this branch.\n     |- Try 55 - 1 = 54. Evaluate 54 != 40, drop this branch.\n     |- Try 55 * 1 = 55. Evaluate 55 != 40, drop this branch.\n     |- Try 55 \/ 1 = 55. Evaluate 55 != 40, drop this branch.\n    |- Try 34 - 21 = 13. Add 13 to the number set. Current number set: [13, 1], target: 40, just two numbers left.\n     |- Try 13 + 1 = 14. Evaluate 14 != 40, drop this branch.\n     |- Try 13 - 1 = 12. Evaluate 12 != 40, drop this branch.\n     |- Try 13 * 1 = 13. Evaluate 13 != 40, drop this branch.\n     |- Try 13 \/ 1 = 13. Evaluate 13 != 40, drop this branch.\n    |- Try 34 * 21 = 714. Add 714 to the number set. Current number set: [714, 1], target: 40, just two numbers left.\n     |- Try 714 + 1 = 715. Evaluate 715 != 40, drop this branch.\n     |- Try 714 - 1 = 713. Evaluate 713 != 40, drop this branch.\n     |- Try 714 * 1 = 714. Evaluate 714 != 40, drop this branch.\n     |- Try 714 \/ 1 = 714. Evaluate 714 != 40, drop this branch.\n    |- Try 34 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (21, 1) (numbers left: [34]). Try possible operations.\n    |- Try 21 + 1 = 22. Add 22 to the number set. Current number set: [22, 34], target: 40, just two numbers left.\n     |- Try 34 + 22 = 56. Evaluate 56 != 40, drop this branch.\n     |- Try 34 - 22 = 12. Evaluate 12 != 40, drop this branch.\n     |- Try 34 * 22 = 748. Evaluate 748 != 40, drop this branch.\n     |- Try 34 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 21 - 1 = 20. Add 20 to the number set. Current number set: [20, 34], target: 40, just two numbers left.\n     |- Try 34 + 20 = 54. Evaluate 54 != 40, drop this branch.\n     |- Try 34 - 20 = 14. Evaluate 14 != 40, drop this branch.\n     |- Try 34 * 20 = 680. Evaluate 680 != 40, drop this branch.\n     |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 * 1 = 21. Add 21 to the number set. Current number set: [21, 34], target: 40, just two numbers left.\n     |- Try 34 + 21 = 55. Evaluate 55 != 40, drop this branch.\n     |- Try 34 - 21 = 13. Evaluate 13 != 40, drop this branch.\n     |- Try 34 * 21 = 714. Evaluate 714 != 40, drop this branch.\n     |- Try 34 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 21 \/ 1 = 21. Add 21 to the number set. Current number set: [21, 34], target: 40, just two numbers left.\n     |- Try 34 + 21 = 55. Evaluate 55 != 40, drop this branch.\n     |- Try 34 - 21 = 13. Evaluate 13 != 40, drop this branch.\n     |- Try 34 * 21 = 714. Evaluate 714 != 40, drop this branch.\n     |- Try 34 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (34, 1) (numbers left: [21]). Try possible operations.\n    |- Try 34 + 1 = 35. Add 35 to the number set. Current number set: [35, 21], target: 40, just two numbers left.\n     |- Try 35 + 21 = 56. Evaluate 56 != 40, drop this branch.\n     |- Try 35 - 21 = 14. Evaluate 14 != 40, drop this branch.\n     |- Try 35 * 21 = 735. Evaluate 735 != 40, drop this branch.\n     |- Try 35 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 34 - 1 = 33. Add 33 to the number set. Current number set: [33, 21], target: 40, just two numbers left.\n     |- Try 33 + 21 = 54. Evaluate 54 != 40, drop this branch.\n     |- Try 33 - 21 = 12. Evaluate 12 != 40, drop this branch.\n     |- Try 33 * 21 = 693. Evaluate 693 != 40, drop this branch.\n     |- Try 33 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 34 * 1 = 34. Add 34 to the number set. Current number set: [34, 21], target: 40, just two numbers left.\n     |- Try 34 + 21 = 55. Evaluate 55 != 40, drop this branch.\n     |- Try 34 - 21 = 13. Evaluate 13 != 40, drop this branch.\n     |- Try 34 * 21 = 714. Evaluate 714 != 40, drop this branch.\n     |- Try 34 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 34 \/ 1 = 34. Add 34 to the number set. Current number set: [34, 21], target: 40, just two numbers left.\n     |- Try 34 + 21 = 55. Evaluate 55 != 40, drop this branch.\n     |- Try 34 - 21 = 13. Evaluate 13 != 40, drop this branch.\n     |- Try 34 * 21 = 714. Evaluate 714 != 40, drop this branch.\n     |- Try 34 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 14 - 7 = 7. Add 7 to the number set. Current number set: [7, 34, 1], target: 40. Options for choosing two numbers: [(7, 34), (7, 1), (34, 1)].\n   |- Pick two numbers (7, 34) (numbers left: [1]). Try possible operations.\n    |- Try 34 + 7 = 41. Add 41 to the number set. Current number set: [41, 1], target: 40, just two numbers left.\n     |- Try 41 + 1 = 42. Evaluate 42 != 40, drop this branch.\n     |- Try 41 - 1 = 40. Evaluate 40 == 40, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 - 1 = 40\nThe step before: 34 + 7 = 41\nThe first step: 14 - 7 = 7\n\nOutput the solution in the required format:\n<Solution>\n14 - 7 = 7\n34 + 7 = 41\n41 - 1 = 40\n<\/Solution>\n","item":{"nums":[7,14,34,1],"solution":["14 - 7 = 7","34 + 7 = 41","41 - 1 = 40"],"target":40}}
+{"instance_id":"countdown_2k_141","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 47, 26, 20]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [32, 47, 26, 20], target: 21. Options for choosing two numbers: [(32, 47), (32, 26), (32, 20), (47, 26), (47, 20), (26, 20)].\n |- Pick two numbers (32, 47) (numbers left: [26, 20]). Try possible operations.\n  |- Try 47 + 32 = 79. Add 79 to the number set. Current number set: [79, 26, 20], target: 21. Options for choosing two numbers: [(79, 26), (79, 20), (26, 20)].\n   |- Pick two numbers (79, 26) (numbers left: [20]). Try possible operations.\n    |- Try 79 + 26 = 105. Add 105 to the number set. Current number set: [105, 20], target: 21, just two numbers left.\n     |- Try 105 + 20 = 125. Evaluate 125 != 21, drop this branch.\n     |- Try 105 - 20 = 85. Evaluate 85 != 21, drop this branch.\n     |- Try 105 * 20 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 20 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 79 - 26 = 53. Add 53 to the number set. Current number set: [53, 20], target: 21, just two numbers left.\n     |- Try 53 + 20 = 73. Evaluate 73 != 21, drop this branch.\n     |- Try 53 - 20 = 33. Evaluate 33 != 21, drop this branch.\n     |- Try 53 * 20 = 1060. Evaluate 1060 != 21, drop this branch.\n     |- Try 53 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 79 * 26 = 2054. 2054 exceeds the maximum intermediate result, drop this branch.\n    |- Try 79 \/ 26 = 3.0. 3.0 is a decimal, drop this branch.\n   |- Pick two numbers (79, 20) (numbers left: [26]). Try possible operations.\n    |- Try 79 + 20 = 99. Add 99 to the number set. Current number set: [99, 26], target: 21, just two numbers left.\n     |- Try 99 + 26 = 125. Evaluate 125 != 21, drop this branch.\n     |- Try 99 - 26 = 73. Evaluate 73 != 21, drop this branch.\n     |- Try 99 * 26 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 26 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 79 - 20 = 59. Add 59 to the number set. Current number set: [59, 26], target: 21, just two numbers left.\n     |- Try 59 + 26 = 85. Evaluate 85 != 21, drop this branch.\n     |- Try 59 - 26 = 33. Evaluate 33 != 21, drop this branch.\n     |- Try 59 * 26 = 1534. Evaluate 1534 != 21, drop this branch.\n     |- Try 59 \/ 26 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 79 * 20 = 1580. Add 1580 to the number set. Current number set: [1580, 26], target: 21, just two numbers left.\n     |- Try 1580 + 26 = 1606. Evaluate 1606 != 21, drop this branch.\n     |- Try 1580 - 26 = 1554. Evaluate 1554 != 21, drop this branch.\n     |- Try 1580 * 26 = 41080. 41080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1580 \/ 26 = 60.8. 60.8 is a decimal, drop this branch.\n    |- Try 79 \/ 20 = 4.0. 4.0 is a decimal, drop this branch.\n   |- Pick two numbers (26, 20) (numbers left: [79]). Try possible operations.\n    |- Try 26 + 20 = 46. Add 46 to the number set. Current number set: [46, 79], target: 21, just two numbers left.\n     |- Try 79 + 46 = 125. Evaluate 125 != 21, drop this branch.\n     |- Try 79 - 46 = 33. Evaluate 33 != 21, drop this branch.\n     |- Try 79 * 46 = 3634. 3634 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 46 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 26 - 20 = 6. Add 6 to the number set. Current number set: [6, 79], target: 21, just two numbers left.\n     |- Try 79 + 6 = 85. Evaluate 85 != 21, drop this branch.\n     |- Try 79 - 6 = 73. Evaluate 73 != 21, drop this branch.\n     |- Try 79 * 6 = 474. Evaluate 474 != 21, drop this branch.\n     |- Try 79 \/ 6 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 26 * 20 = 520. Add 520 to the number set. Current number set: [520, 79], target: 21, just two numbers left.\n     |- Try 520 + 79 = 599. Evaluate 599 != 21, drop this branch.\n     |- Try 520 - 79 = 441. Evaluate 441 != 21, drop this branch.\n     |- Try 520 * 79 = 41080. 41080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 520 \/ 79 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 26 \/ 20 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 47 - 32 = 15. Add 15 to the number set. Current number set: [15, 26, 20], target: 21. Options for choosing two numbers: [(15, 26), (15, 20), (26, 20)].\n   |- Pick two numbers (15, 26) (numbers left: [20]). Try possible operations.\n    |- Try 26 + 15 = 41. Add 41 to the number set. Current number set: [41, 20], target: 21, just two numbers left.\n     |- Try 41 + 20 = 61. Evaluate 61 != 21, drop this branch.\n     |- Try 41 - 20 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 - 20 = 21\nThe step before: 26 + 15 = 41\nThe first step: 47 - 32 = 15\n\nOutput the solution in the required format:\n<Solution>\n47 - 32 = 15\n26 + 15 = 41\n41 - 20 = 21\n<\/Solution>\n","item":{"nums":[32,47,26,20],"solution":["47 - 32 = 15","26 + 15 = 41","41 - 20 = 21"],"target":21}}
+{"instance_id":"countdown_2k_142","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 41, 47, 26]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [10, 41, 47, 26], target: 42. Options for choosing two numbers: [(10, 41), (10, 47), (10, 26), (41, 47), (41, 26), (47, 26)].\n |- Pick two numbers (10, 41) (numbers left: [47, 26]). Try possible operations.\n  |- Try 41 + 10 = 51. Add 51 to the number set. Current number set: [51, 47, 26], target: 42. Options for choosing two numbers: [(51, 47), (51, 26), (47, 26)].\n   |- Pick two numbers (51, 47) (numbers left: [26]). Try possible operations.\n    |- Try 51 + 47 = 98. Add 98 to the number set. Current number set: [98, 26], target: 42, just two numbers left.\n     |- Try 98 + 26 = 124. Evaluate 124 != 42, drop this branch.\n     |- Try 98 - 26 = 72. Evaluate 72 != 42, drop this branch.\n     |- Try 98 * 26 = 2548. 2548 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 26 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 51 - 47 = 4. Add 4 to the number set. Current number set: [4, 26], target: 42, just two numbers left.\n     |- Try 26 + 4 = 30. Evaluate 30 != 42, drop this branch.\n     |- Try 26 - 4 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 26 * 4 = 104. Evaluate 104 != 42, drop this branch.\n     |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 51 * 47 = 2397. 2397 exceeds the maximum intermediate result, drop this branch.\n    |- Try 51 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (51, 26) (numbers left: [47]). Try possible operations.\n    |- Try 51 + 26 = 77. Add 77 to the number set. Current number set: [77, 47], target: 42, just two numbers left.\n     |- Try 77 + 47 = 124. Evaluate 124 != 42, drop this branch.\n     |- Try 77 - 47 = 30. Evaluate 30 != 42, drop this branch.\n     |- Try 77 * 47 = 3619. 3619 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 47 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 51 - 26 = 25. Add 25 to the number set. Current number set: [25, 47], target: 42, just two numbers left.\n     |- Try 47 + 25 = 72. Evaluate 72 != 42, drop this branch.\n     |- Try 47 - 25 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 47 * 25 = 1175. Evaluate 1175 != 42, drop this branch.\n     |- Try 47 \/ 25 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 51 * 26 = 1326. Add 1326 to the number set. Current number set: [1326, 47], target: 42, just two numbers left.\n     |- Try 1326 + 47 = 1373. Evaluate 1373 != 42, drop this branch.\n     |- Try 1326 - 47 = 1279. Evaluate 1279 != 42, drop this branch.\n     |- Try 1326 * 47 = 62322. 62322 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1326 \/ 47 = 28.2. 28.2 is a decimal, drop this branch.\n    |- Try 51 \/ 26 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (47, 26) (numbers left: [51]). Try possible operations.\n    |- Try 47 + 26 = 73. Add 73 to the number set. Current number set: [73, 51], target: 42, just two numbers left.\n     |- Try 73 + 51 = 124. Evaluate 124 != 42, drop this branch.\n     |- Try 73 - 51 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 73 * 51 = 3723. 3723 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 51 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 47 - 26 = 21. Add 21 to the number set. Current number set: [21, 51], target: 42, just two numbers left.\n     |- Try 51 + 21 = 72. Evaluate 72 != 42, drop this branch.\n     |- Try 51 - 21 = 30. Evaluate 30 != 42, drop this branch.\n     |- Try 51 * 21 = 1071. Evaluate 1071 != 42, drop this branch.\n     |- Try 51 \/ 21 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 47 * 26 = 1222. Add 1222 to the number set. Current number set: [1222, 51], target: 42, just two numbers left.\n     |- Try 1222 + 51 = 1273. Evaluate 1273 != 42, drop this branch.\n     |- Try 1222 - 51 = 1171. Evaluate 1171 != 42, drop this branch.\n     |- Try 1222 * 51 = 62322. 62322 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1222 \/ 51 = 24.0. 24.0 is a decimal, drop this branch.\n    |- Try 47 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 41 - 10 = 31. Add 31 to the number set. Current number set: [31, 47, 26], target: 42. Options for choosing two numbers: [(31, 47), (31, 26), (47, 26)].\n   |- Pick two numbers (31, 47) (numbers left: [26]). Try possible operations.\n    |- Try 47 + 31 = 78. Add 78 to the number set. Current number set: [78, 26], target: 42, just two numbers left.\n     |- Try 78 + 26 = 104. Evaluate 104 != 42, drop this branch.\n     |- Try 78 - 26 = 52. Evaluate 52 != 42, drop this branch.\n     |- Try 78 * 26 = 2028. 2028 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 26 = 3. Evaluate 3 != 42, drop this branch.\n    |- Try 47 - 31 = 16. Add 16 to the number set. Current number set: [16, 26], target: 42, just two numbers left.\n     |- Try 26 + 16 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 + 16 = 42\nThe step before: 47 - 31 = 16\nThe first step: 41 - 10 = 31\n\nOutput the solution in the required format:\n<Solution>\n41 - 10 = 31\n47 - 31 = 16\n26 + 16 = 42\n<\/Solution>\n","item":{"nums":[10,41,47,26],"solution":["41 - 10 = 31","47 - 31 = 16","26 + 16 = 42"],"target":42}}
+{"instance_id":"countdown_2k_143","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 2, 38, 37]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [15, 2, 38, 37], target: 17. Options for choosing two numbers: [(15, 2), (15, 38), (15, 37), (2, 38), (2, 37), (38, 37)].\n |- Pick two numbers (15, 2) (numbers left: [38, 37]). Try possible operations.\n  |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 38, 37], target: 17. Options for choosing two numbers: [(17, 38), (17, 37), (38, 37)].\n   |- Pick two numbers (17, 38) (numbers left: [37]). Try possible operations.\n    |- Try 38 + 17 = 55. Add 55 to the number set. Current number set: [55, 37], target: 17, just two numbers left.\n     |- Try 55 + 37 = 92. Evaluate 92 != 17, drop this branch.\n     |- Try 55 - 37 = 18. Evaluate 18 != 17, drop this branch.\n     |- Try 55 * 37 = 2035. 2035 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 37 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 38 - 17 = 21. Add 21 to the number set. Current number set: [21, 37], target: 17, just two numbers left.\n     |- Try 37 + 21 = 58. Evaluate 58 != 17, drop this branch.\n     |- Try 37 - 21 = 16. Evaluate 16 != 17, drop this branch.\n     |- Try 37 * 21 = 777. Evaluate 777 != 17, drop this branch.\n     |- Try 37 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 38 * 17 = 646. Add 646 to the number set. Current number set: [646, 37], target: 17, just two numbers left.\n     |- Try 646 + 37 = 683. Evaluate 683 != 17, drop this branch.\n     |- Try 646 - 37 = 609. Evaluate 609 != 17, drop this branch.\n     |- Try 646 * 37 = 23902. 23902 exceeds the maximum intermediate result, drop this branch.\n     |- Try 646 \/ 37 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 38 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (17, 37) (numbers left: [38]). Try possible operations.\n    |- Try 37 + 17 = 54. Add 54 to the number set. Current number set: [54, 38], target: 17, just two numbers left.\n     |- Try 54 + 38 = 92. Evaluate 92 != 17, drop this branch.\n     |- Try 54 - 38 = 16. Evaluate 16 != 17, drop this branch.\n     |- Try 54 * 38 = 2052. 2052 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 38 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 - 17 = 20. Add 20 to the number set. Current number set: [20, 38], target: 17, just two numbers left.\n     |- Try 38 + 20 = 58. Evaluate 58 != 17, drop this branch.\n     |- Try 38 - 20 = 18. Evaluate 18 != 17, drop this branch.\n     |- Try 38 * 20 = 760. Evaluate 760 != 17, drop this branch.\n     |- Try 38 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 37 * 17 = 629. Add 629 to the number set. Current number set: [629, 38], target: 17, just two numbers left.\n     |- Try 629 + 38 = 667. Evaluate 667 != 17, drop this branch.\n     |- Try 629 - 38 = 591. Evaluate 591 != 17, drop this branch.\n     |- Try 629 * 38 = 23902. 23902 exceeds the maximum intermediate result, drop this branch.\n     |- Try 629 \/ 38 = 16.6. 16.6 is a decimal, drop this branch.\n    |- Try 37 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (38, 37) (numbers left: [17]). Try possible operations.\n    |- Try 38 + 37 = 75. Add 75 to the number set. Current number set: [75, 17], target: 17, just two numbers left.\n     |- Try 75 + 17 = 92. Evaluate 92 != 17, drop this branch.\n     |- Try 75 - 17 = 58. Evaluate 58 != 17, drop this branch.\n     |- Try 75 * 17 = 1275. Evaluate 1275 != 17, drop this branch.\n     |- Try 75 \/ 17 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 38 - 37 = 1. Add 1 to the number set. Current number set: [1, 17], target: 17, just two numbers left.\n     |- Try 17 + 1 = 18. Evaluate 18 != 17, drop this branch.\n     |- Try 17 - 1 = 16. Evaluate 16 != 17, drop this branch.\n     |- Try 17 * 1 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 17 * 1 = 17\nThe step before: 38 - 37 = 1\nThe first step: 15 + 2 = 17\n\nOutput the solution in the required format:\n<Solution>\n15 + 2 = 17\n38 - 37 = 1\n17 * 1 = 17\n<\/Solution>\n","item":{"nums":[15,2,38,37],"solution":["15 + 2 = 17","38 - 37 = 1","17 * 1 = 17"],"target":17}}
+{"instance_id":"countdown_2k_144","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 33, 39, 11]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [42, 33, 39, 11], target: 37. Options for choosing two numbers: [(42, 33), (42, 39), (42, 11), (33, 39), (33, 11), (39, 11)].\n |- Pick two numbers (42, 33) (numbers left: [39, 11]). Try possible operations.\n  |- Try 42 + 33 = 75. Add 75 to the number set. Current number set: [75, 39, 11], target: 37. Options for choosing two numbers: [(75, 39), (75, 11), (39, 11)].\n   |- Pick two numbers (75, 39) (numbers left: [11]). Try possible operations.\n    |- Try 75 + 39 = 114. Add 114 to the number set. Current number set: [114, 11], target: 37, just two numbers left.\n     |- Try 114 + 11 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 114 - 11 = 103. Evaluate 103 != 37, drop this branch.\n     |- Try 114 * 11 = 1254. Evaluate 1254 != 37, drop this branch.\n     |- Try 114 \/ 11 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 75 - 39 = 36. Add 36 to the number set. Current number set: [36, 11], target: 37, just two numbers left.\n     |- Try 36 + 11 = 47. Evaluate 47 != 37, drop this branch.\n     |- Try 36 - 11 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 36 * 11 = 396. Evaluate 396 != 37, drop this branch.\n     |- Try 36 \/ 11 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 75 * 39 = 2925. 2925 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 39 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (75, 11) (numbers left: [39]). Try possible operations.\n    |- Try 75 + 11 = 86. Add 86 to the number set. Current number set: [86, 39], target: 37, just two numbers left.\n     |- Try 86 + 39 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 86 - 39 = 47. Evaluate 47 != 37, drop this branch.\n     |- Try 86 * 39 = 3354. 3354 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 39 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 75 - 11 = 64. Add 64 to the number set. Current number set: [64, 39], target: 37, just two numbers left.\n     |- Try 64 + 39 = 103. Evaluate 103 != 37, drop this branch.\n     |- Try 64 - 39 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 64 * 39 = 2496. 2496 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 39 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 75 * 11 = 825. Add 825 to the number set. Current number set: [825, 39], target: 37, just two numbers left.\n     |- Try 825 + 39 = 864. Evaluate 864 != 37, drop this branch.\n     |- Try 825 - 39 = 786. Evaluate 786 != 37, drop this branch.\n     |- Try 825 * 39 = 32175. 32175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 825 \/ 39 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 75 \/ 11 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (39, 11) (numbers left: [75]). Try possible operations.\n    |- Try 39 + 11 = 50. Add 50 to the number set. Current number set: [50, 75], target: 37, just two numbers left.\n     |- Try 75 + 50 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 75 - 50 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 75 * 50 = 3750. 3750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 50 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 - 11 = 28. Add 28 to the number set. Current number set: [28, 75], target: 37, just two numbers left.\n     |- Try 75 + 28 = 103. Evaluate 103 != 37, drop this branch.\n     |- Try 75 - 28 = 47. Evaluate 47 != 37, drop this branch.\n     |- Try 75 * 28 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 28 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 39 * 11 = 429. Add 429 to the number set. Current number set: [429, 75], target: 37, just two numbers left.\n     |- Try 429 + 75 = 504. Evaluate 504 != 37, drop this branch.\n     |- Try 429 - 75 = 354. Evaluate 354 != 37, drop this branch.\n     |- Try 429 * 75 = 32175. 32175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 429 \/ 75 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 39 \/ 11 = 3.5. 3.5 is a decimal, drop this branch.\n  |- Try 42 - 33 = 9. Add 9 to the number set. Current number set: [9, 39, 11], target: 37. Options for choosing two numbers: [(9, 39), (9, 11), (39, 11)].\n   |- Pick two numbers (9, 39) (numbers left: [11]). Try possible operations.\n    |- Try 39 + 9 = 48. Add 48 to the number set. Current number set: [48, 11], target: 37, just two numbers left.\n     |- Try 48 + 11 = 59. Evaluate 59 != 37, drop this branch.\n     |- Try 48 - 11 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 11 = 37\nThe step before: 39 + 9 = 48\nThe first step: 42 - 33 = 9\n\nOutput the solution in the required format:\n<Solution>\n42 - 33 = 9\n39 + 9 = 48\n48 - 11 = 37\n<\/Solution>\n","item":{"nums":[42,33,39,11],"solution":["42 - 33 = 9","39 + 9 = 48","48 - 11 = 37"],"target":37}}
+{"instance_id":"countdown_2k_145","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 39, 7, 4]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [18, 39, 7, 4], target: 32. Options for choosing two numbers: [(18, 39), (18, 7), (18, 4), (39, 7), (39, 4), (7, 4)].\n |- Pick two numbers (18, 39) (numbers left: [7, 4]). Try possible operations.\n  |- Try 39 + 18 = 57. Add 57 to the number set. Current number set: [57, 7, 4], target: 32. Options for choosing two numbers: [(57, 7), (57, 4), (7, 4)].\n   |- Pick two numbers (57, 7) (numbers left: [4]). Try possible operations.\n    |- Try 57 + 7 = 64. Add 64 to the number set. Current number set: [64, 4], target: 32, just two numbers left.\n     |- Try 64 + 4 = 68. Evaluate 68 != 32, drop this branch.\n     |- Try 64 - 4 = 60. Evaluate 60 != 32, drop this branch.\n     |- Try 64 * 4 = 256. Evaluate 256 != 32, drop this branch.\n     |- Try 64 \/ 4 = 16. Evaluate 16 != 32, drop this branch.\n    |- Try 57 - 7 = 50. Add 50 to the number set. Current number set: [50, 4], target: 32, just two numbers left.\n     |- Try 50 + 4 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 50 - 4 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 50 * 4 = 200. Evaluate 200 != 32, drop this branch.\n     |- Try 50 \/ 4 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 57 * 7 = 399. Add 399 to the number set. Current number set: [399, 4], target: 32, just two numbers left.\n     |- Try 399 + 4 = 403. Evaluate 403 != 32, drop this branch.\n     |- Try 399 - 4 = 395. Evaluate 395 != 32, drop this branch.\n     |- Try 399 * 4 = 1596. Evaluate 1596 != 32, drop this branch.\n     |- Try 399 \/ 4 = 99.8. 99.8 is a decimal, drop this branch.\n    |- Try 57 \/ 7 = 8.1. 8.1 is a decimal, drop this branch.\n   |- Pick two numbers (57, 4) (numbers left: [7]). Try possible operations.\n    |- Try 57 + 4 = 61. Add 61 to the number set. Current number set: [61, 7], target: 32, just two numbers left.\n     |- Try 61 + 7 = 68. Evaluate 68 != 32, drop this branch.\n     |- Try 61 - 7 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 61 * 7 = 427. Evaluate 427 != 32, drop this branch.\n     |- Try 61 \/ 7 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 57 - 4 = 53. Add 53 to the number set. Current number set: [53, 7], target: 32, just two numbers left.\n     |- Try 53 + 7 = 60. Evaluate 60 != 32, drop this branch.\n     |- Try 53 - 7 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 53 * 7 = 371. Evaluate 371 != 32, drop this branch.\n     |- Try 53 \/ 7 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 57 * 4 = 228. Add 228 to the number set. Current number set: [228, 7], target: 32, just two numbers left.\n     |- Try 228 + 7 = 235. Evaluate 235 != 32, drop this branch.\n     |- Try 228 - 7 = 221. Evaluate 221 != 32, drop this branch.\n     |- Try 228 * 7 = 1596. Evaluate 1596 != 32, drop this branch.\n     |- Try 228 \/ 7 = 32.6. 32.6 is a decimal, drop this branch.\n    |- Try 57 \/ 4 = 14.2. 14.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 4) (numbers left: [57]). Try possible operations.\n    |- Try 7 + 4 = 11. Add 11 to the number set. Current number set: [11, 57], target: 32, just two numbers left.\n     |- Try 57 + 11 = 68. Evaluate 68 != 32, drop this branch.\n     |- Try 57 - 11 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 57 * 11 = 627. Evaluate 627 != 32, drop this branch.\n     |- Try 57 \/ 11 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 7 - 4 = 3. Add 3 to the number set. Current number set: [3, 57], target: 32, just two numbers left.\n     |- Try 57 + 3 = 60. Evaluate 60 != 32, drop this branch.\n     |- Try 57 - 3 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 57 * 3 = 171. Evaluate 171 != 32, drop this branch.\n     |- Try 57 \/ 3 = 19. Evaluate 19 != 32, drop this branch.\n    |- Try 7 * 4 = 28. Add 28 to the number set. Current number set: [28, 57], target: 32, just two numbers left.\n     |- Try 57 + 28 = 85. Evaluate 85 != 32, drop this branch.\n     |- Try 57 - 28 = 29. Evaluate 29 != 32, drop this branch.\n     |- Try 57 * 28 = 1596. Evaluate 1596 != 32, drop this branch.\n     |- Try 57 \/ 28 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 39 - 18 = 21. Add 21 to the number set. Current number set: [21, 7, 4], target: 32. Options for choosing two numbers: [(21, 7), (21, 4), (7, 4)].\n   |- Pick two numbers (21, 7) (numbers left: [4]). Try possible operations.\n    |- Try 21 + 7 = 28. Add 28 to the number set. Current number set: [28, 4], target: 32, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 + 4 = 32\nThe step before: 21 + 7 = 28\nThe first step: 39 - 18 = 21\n\nOutput the solution in the required format:\n<Solution>\n39 - 18 = 21\n21 + 7 = 28\n28 + 4 = 32\n<\/Solution>\n","item":{"nums":[18,39,7,4],"solution":["39 - 18 = 21","21 + 7 = 28","28 + 4 = 32"],"target":32}}
+{"instance_id":"countdown_2k_146","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [16, 6, 11, 37]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [16, 6, 11, 37], target: 38. Options for choosing two numbers: [(16, 6), (16, 11), (16, 37), (6, 11), (6, 37), (11, 37)].\n |- Pick two numbers (16, 6) (numbers left: [11, 37]). Try possible operations.\n  |- Try 16 + 6 = 22. Add 22 to the number set. Current number set: [22, 11, 37], target: 38. Options for choosing two numbers: [(22, 11), (22, 37), (11, 37)].\n   |- Pick two numbers (22, 11) (numbers left: [37]). Try possible operations.\n    |- Try 22 + 11 = 33. Add 33 to the number set. Current number set: [33, 37], target: 38, just two numbers left.\n     |- Try 37 + 33 = 70. Evaluate 70 != 38, drop this branch.\n     |- Try 37 - 33 = 4. Evaluate 4 != 38, drop this branch.\n     |- Try 37 * 33 = 1221. Evaluate 1221 != 38, drop this branch.\n     |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 - 11 = 11. Add 11 to the number set. Current number set: [11, 37], target: 38, just two numbers left.\n     |- Try 37 + 11 = 48. Evaluate 48 != 38, drop this branch.\n     |- Try 37 - 11 = 26. Evaluate 26 != 38, drop this branch.\n     |- Try 37 * 11 = 407. Evaluate 407 != 38, drop this branch.\n     |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 22 * 11 = 242. Add 242 to the number set. Current number set: [242, 37], target: 38, just two numbers left.\n     |- Try 242 + 37 = 279. Evaluate 279 != 38, drop this branch.\n     |- Try 242 - 37 = 205. Evaluate 205 != 38, drop this branch.\n     |- Try 242 * 37 = 8954. 8954 exceeds the maximum intermediate result, drop this branch.\n     |- Try 242 \/ 37 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 22 \/ 11 = 2. Add 2 to the number set. Current number set: [2, 37], target: 38, just two numbers left.\n     |- Try 37 + 2 = 39. Evaluate 39 != 38, drop this branch.\n     |- Try 37 - 2 = 35. Evaluate 35 != 38, drop this branch.\n     |- Try 37 * 2 = 74. Evaluate 74 != 38, drop this branch.\n     |- Try 37 \/ 2 = 18.5. 18.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 37) (numbers left: [11]). Try possible operations.\n    |- Try 37 + 22 = 59. Add 59 to the number set. Current number set: [59, 11], target: 38, just two numbers left.\n     |- Try 59 + 11 = 70. Evaluate 70 != 38, drop this branch.\n     |- Try 59 - 11 = 48. Evaluate 48 != 38, drop this branch.\n     |- Try 59 * 11 = 649. Evaluate 649 != 38, drop this branch.\n     |- Try 59 \/ 11 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 37 - 22 = 15. Add 15 to the number set. Current number set: [15, 11], target: 38, just two numbers left.\n     |- Try 15 + 11 = 26. Evaluate 26 != 38, drop this branch.\n     |- Try 15 - 11 = 4. Evaluate 4 != 38, drop this branch.\n     |- Try 15 * 11 = 165. Evaluate 165 != 38, drop this branch.\n     |- Try 15 \/ 11 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 * 22 = 814. Add 814 to the number set. Current number set: [814, 11], target: 38, just two numbers left.\n     |- Try 814 + 11 = 825. Evaluate 825 != 38, drop this branch.\n     |- Try 814 - 11 = 803. Evaluate 803 != 38, drop this branch.\n     |- Try 814 * 11 = 8954. 8954 exceeds the maximum intermediate result, drop this branch.\n     |- Try 814 \/ 11 = 74. Evaluate 74 != 38, drop this branch.\n    |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (11, 37) (numbers left: [22]). Try possible operations.\n    |- Try 37 + 11 = 48. Add 48 to the number set. Current number set: [48, 22], target: 38, just two numbers left.\n     |- Try 48 + 22 = 70. Evaluate 70 != 38, drop this branch.\n     |- Try 48 - 22 = 26. Evaluate 26 != 38, drop this branch.\n     |- Try 48 * 22 = 1056. Evaluate 1056 != 38, drop this branch.\n     |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 37 - 11 = 26. Add 26 to the number set. Current number set: [26, 22], target: 38, just two numbers left.\n     |- Try 26 + 22 = 48. Evaluate 48 != 38, drop this branch.\n     |- Try 26 - 22 = 4. Evaluate 4 != 38, drop this branch.\n     |- Try 26 * 22 = 572. Evaluate 572 != 38, drop this branch.\n     |- Try 26 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 * 11 = 407. Add 407 to the number set. Current number set: [407, 22], target: 38, just two numbers left.\n     |- Try 407 + 22 = 429. Evaluate 429 != 38, drop this branch.\n     |- Try 407 - 22 = 385. Evaluate 385 != 38, drop this branch.\n     |- Try 407 * 22 = 8954. 8954 exceeds the maximum intermediate result, drop this branch.\n     |- Try 407 \/ 22 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n  |- Try 16 - 6 = 10. Add 10 to the number set. Current number set: [10, 11, 37], target: 38. Options for choosing two numbers: [(10, 11), (10, 37), (11, 37)].\n   |- Pick two numbers (10, 11) (numbers left: [37]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 37], target: 38, just two numbers left.\n     |- Try 37 + 21 = 58. Evaluate 58 != 38, drop this branch.\n     |- Try 37 - 21 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 37 * 21 = 777. Evaluate 777 != 38, drop this branch.\n     |- Try 37 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 37], target: 38, just two numbers left.\n     |- Try 37 + 1 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 37 + 1 = 38\nThe step before: 11 - 10 = 1\nThe first step: 16 - 6 = 10\n\nOutput the solution in the required format:\n<Solution>\n16 - 6 = 10\n11 - 10 = 1\n37 + 1 = 38\n<\/Solution>\n","item":{"nums":[16,6,11,37],"solution":["16 - 6 = 10","11 - 10 = 1","37 + 1 = 38"],"target":38}}
+{"instance_id":"countdown_2k_147","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 48, 19, 36]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [6, 48, 19, 36], target: 13. Options for choosing two numbers: [(6, 48), (6, 19), (6, 36), (48, 19), (48, 36), (19, 36)].\n |- Pick two numbers (6, 48) (numbers left: [19, 36]). Try possible operations.\n  |- Try 48 + 6 = 54. Add 54 to the number set. Current number set: [54, 19, 36], target: 13. Options for choosing two numbers: [(54, 19), (54, 36), (19, 36)].\n   |- Pick two numbers (54, 19) (numbers left: [36]). Try possible operations.\n    |- Try 54 + 19 = 73. Add 73 to the number set. Current number set: [73, 36], target: 13, just two numbers left.\n     |- Try 73 + 36 = 109. Evaluate 109 != 13, drop this branch.\n     |- Try 73 - 36 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 73 * 36 = 2628. 2628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 36 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 54 - 19 = 35. Add 35 to the number set. Current number set: [35, 36], target: 13, just two numbers left.\n     |- Try 36 + 35 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 36 - 35 = 1. Evaluate 1 != 13, drop this branch.\n     |- Try 36 * 35 = 1260. Evaluate 1260 != 13, drop this branch.\n     |- Try 36 \/ 35 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 54 * 19 = 1026. Add 1026 to the number set. Current number set: [1026, 36], target: 13, just two numbers left.\n     |- Try 1026 + 36 = 1062. Evaluate 1062 != 13, drop this branch.\n     |- Try 1026 - 36 = 990. Evaluate 990 != 13, drop this branch.\n     |- Try 1026 * 36 = 36936. 36936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1026 \/ 36 = 28.5. 28.5 is a decimal, drop this branch.\n    |- Try 54 \/ 19 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (54, 36) (numbers left: [19]). Try possible operations.\n    |- Try 54 + 36 = 90. Add 90 to the number set. Current number set: [90, 19], target: 13, just two numbers left.\n     |- Try 90 + 19 = 109. Evaluate 109 != 13, drop this branch.\n     |- Try 90 - 19 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 90 * 19 = 1710. Evaluate 1710 != 13, drop this branch.\n     |- Try 90 \/ 19 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 54 - 36 = 18. Add 18 to the number set. Current number set: [18, 19], target: 13, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 13, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 13, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 54 * 36 = 1944. Add 1944 to the number set. Current number set: [1944, 19], target: 13, just two numbers left.\n     |- Try 1944 + 19 = 1963. Evaluate 1963 != 13, drop this branch.\n     |- Try 1944 - 19 = 1925. Evaluate 1925 != 13, drop this branch.\n     |- Try 1944 * 19 = 36936. 36936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1944 \/ 19 = 102.3. 102.3 is a decimal, drop this branch.\n    |- Try 54 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (19, 36) (numbers left: [54]). Try possible operations.\n    |- Try 36 + 19 = 55. Add 55 to the number set. Current number set: [55, 54], target: 13, just two numbers left.\n     |- Try 55 + 54 = 109. Evaluate 109 != 13, drop this branch.\n     |- Try 55 - 54 = 1. Evaluate 1 != 13, drop this branch.\n     |- Try 55 * 54 = 2970. 2970 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 54 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 19 = 17. Add 17 to the number set. Current number set: [17, 54], target: 13, just two numbers left.\n     |- Try 54 + 17 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 54 - 17 = 37. Evaluate 37 != 13, drop this branch.\n     |- Try 54 * 17 = 918. Evaluate 918 != 13, drop this branch.\n     |- Try 54 \/ 17 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 36 * 19 = 684. Add 684 to the number set. Current number set: [684, 54], target: 13, just two numbers left.\n     |- Try 684 + 54 = 738. Evaluate 738 != 13, drop this branch.\n     |- Try 684 - 54 = 630. Evaluate 630 != 13, drop this branch.\n     |- Try 684 * 54 = 36936. 36936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 54 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 36 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 48 - 6 = 42. Add 42 to the number set. Current number set: [42, 19, 36], target: 13. Options for choosing two numbers: [(42, 19), (42, 36), (19, 36)].\n   |- Pick two numbers (42, 19) (numbers left: [36]). Try possible operations.\n    |- Try 42 + 19 = 61. Add 61 to the number set. Current number set: [61, 36], target: 13, just two numbers left.\n     |- Try 61 + 36 = 97. Evaluate 97 != 13, drop this branch.\n     |- Try 61 - 36 = 25. Evaluate 25 != 13, drop this branch.\n     |- Try 61 * 36 = 2196. 2196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 36 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 42 - 19 = 23. Add 23 to the number set. Current number set: [23, 36], target: 13, just two numbers left.\n     |- Try 36 + 23 = 59. Evaluate 59 != 13, drop this branch.\n     |- Try 36 - 23 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 23 = 13\nThe step before: 42 - 19 = 23\nThe first step: 48 - 6 = 42\n\nOutput the solution in the required format:\n<Solution>\n48 - 6 = 42\n42 - 19 = 23\n36 - 23 = 13\n<\/Solution>\n","item":{"nums":[6,48,19,36],"solution":["48 - 6 = 42","42 - 19 = 23","36 - 23 = 13"],"target":13}}
+{"instance_id":"countdown_2k_148","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 34, 15, 12]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [49, 34, 15, 12], target: 12. Options for choosing two numbers: [(49, 34), (49, 15), (49, 12), (34, 15), (34, 12), (15, 12)].\n |- Pick two numbers (49, 34) (numbers left: [15, 12]). Try possible operations.\n  |- Try 49 + 34 = 83. Add 83 to the number set. Current number set: [83, 15, 12], target: 12. Options for choosing two numbers: [(83, 15), (83, 12), (15, 12)].\n   |- Pick two numbers (83, 15) (numbers left: [12]). Try possible operations.\n    |- Try 83 + 15 = 98. Add 98 to the number set. Current number set: [98, 12], target: 12, just two numbers left.\n     |- Try 98 + 12 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 98 - 12 = 86. Evaluate 86 != 12, drop this branch.\n     |- Try 98 * 12 = 1176. Evaluate 1176 != 12, drop this branch.\n     |- Try 98 \/ 12 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 83 - 15 = 68. Add 68 to the number set. Current number set: [68, 12], target: 12, just two numbers left.\n     |- Try 68 + 12 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 68 - 12 = 56. Evaluate 56 != 12, drop this branch.\n     |- Try 68 * 12 = 816. Evaluate 816 != 12, drop this branch.\n     |- Try 68 \/ 12 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 83 * 15 = 1245. Add 1245 to the number set. Current number set: [1245, 12], target: 12, just two numbers left.\n     |- Try 1245 + 12 = 1257. Evaluate 1257 != 12, drop this branch.\n     |- Try 1245 - 12 = 1233. Evaluate 1233 != 12, drop this branch.\n     |- Try 1245 * 12 = 14940. 14940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1245 \/ 12 = 103.8. 103.8 is a decimal, drop this branch.\n    |- Try 83 \/ 15 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (83, 12) (numbers left: [15]). Try possible operations.\n    |- Try 83 + 12 = 95. Add 95 to the number set. Current number set: [95, 15], target: 12, just two numbers left.\n     |- Try 95 + 15 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 95 - 15 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 95 * 15 = 1425. Evaluate 1425 != 12, drop this branch.\n     |- Try 95 \/ 15 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 83 - 12 = 71. Add 71 to the number set. Current number set: [71, 15], target: 12, just two numbers left.\n     |- Try 71 + 15 = 86. Evaluate 86 != 12, drop this branch.\n     |- Try 71 - 15 = 56. Evaluate 56 != 12, drop this branch.\n     |- Try 71 * 15 = 1065. Evaluate 1065 != 12, drop this branch.\n     |- Try 71 \/ 15 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 83 * 12 = 996. Add 996 to the number set. Current number set: [996, 15], target: 12, just two numbers left.\n     |- Try 996 + 15 = 1011. Evaluate 1011 != 12, drop this branch.\n     |- Try 996 - 15 = 981. Evaluate 981 != 12, drop this branch.\n     |- Try 996 * 15 = 14940. 14940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 996 \/ 15 = 66.4. 66.4 is a decimal, drop this branch.\n    |- Try 83 \/ 12 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (15, 12) (numbers left: [83]). Try possible operations.\n    |- Try 15 + 12 = 27. Add 27 to the number set. Current number set: [27, 83], target: 12, just two numbers left.\n     |- Try 83 + 27 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 83 - 27 = 56. Evaluate 56 != 12, drop this branch.\n     |- Try 83 * 27 = 2241. 2241 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 27 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 15 - 12 = 3. Add 3 to the number set. Current number set: [3, 83], target: 12, just two numbers left.\n     |- Try 83 + 3 = 86. Evaluate 86 != 12, drop this branch.\n     |- Try 83 - 3 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 83 * 3 = 249. Evaluate 249 != 12, drop this branch.\n     |- Try 83 \/ 3 = 27.7. 27.7 is a decimal, drop this branch.\n    |- Try 15 * 12 = 180. Add 180 to the number set. Current number set: [180, 83], target: 12, just two numbers left.\n     |- Try 180 + 83 = 263. Evaluate 263 != 12, drop this branch.\n     |- Try 180 - 83 = 97. Evaluate 97 != 12, drop this branch.\n     |- Try 180 * 83 = 14940. 14940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 83 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 15 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 49 - 34 = 15. Add 15 to the number set. Current number set: [15, 15, 12], target: 12. Options for choosing two numbers: [(15, 15), (15, 12), (15, 12)].\n   |- Pick two numbers (15, 15) (numbers left: [12]). Try possible operations.\n    |- Try 15 + 15 = 30. Add 30 to the number set. Current number set: [30, 12], target: 12, just two numbers left.\n     |- Try 30 + 12 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 30 - 12 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 30 * 12 = 360. Evaluate 360 != 12, drop this branch.\n     |- Try 30 \/ 12 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 15 - 15 = 0. Add 0 to the number set. Current number set: [0, 12], target: 12, just two numbers left.\n     |- Try 12 + 0 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 12 + 0 = 12\nThe step before: 15 - 15 = 0\nThe first step: 49 - 34 = 15\n\nOutput the solution in the required format:\n<Solution>\n49 - 34 = 15\n15 - 15 = 0\n12 + 0 = 12\n<\/Solution>\n","item":{"nums":[49,34,15,12],"solution":["49 - 34 = 15","15 - 15 = 0","12 + 0 = 12"],"target":12}}
+{"instance_id":"countdown_2k_149","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 28, 1, 23]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [48, 28, 1, 23], target: 44. Options for choosing two numbers: [(48, 28), (48, 1), (48, 23), (28, 1), (28, 23), (1, 23)].\n |- Pick two numbers (48, 28) (numbers left: [1, 23]). Try possible operations.\n  |- Try 48 + 28 = 76. Add 76 to the number set. Current number set: [76, 1, 23], target: 44. Options for choosing two numbers: [(76, 1), (76, 23), (1, 23)].\n   |- Pick two numbers (76, 1) (numbers left: [23]). Try possible operations.\n    |- Try 76 + 1 = 77. Add 77 to the number set. Current number set: [77, 23], target: 44, just two numbers left.\n     |- Try 77 + 23 = 100. Evaluate 100 != 44, drop this branch.\n     |- Try 77 - 23 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 77 * 23 = 1771. Evaluate 1771 != 44, drop this branch.\n     |- Try 77 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 76 - 1 = 75. Add 75 to the number set. Current number set: [75, 23], target: 44, just two numbers left.\n     |- Try 75 + 23 = 98. Evaluate 98 != 44, drop this branch.\n     |- Try 75 - 23 = 52. Evaluate 52 != 44, drop this branch.\n     |- Try 75 * 23 = 1725. Evaluate 1725 != 44, drop this branch.\n     |- Try 75 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 76 * 1 = 76. Add 76 to the number set. Current number set: [76, 23], target: 44, just two numbers left.\n     |- Try 76 + 23 = 99. Evaluate 99 != 44, drop this branch.\n     |- Try 76 - 23 = 53. Evaluate 53 != 44, drop this branch.\n     |- Try 76 * 23 = 1748. Evaluate 1748 != 44, drop this branch.\n     |- Try 76 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 76 \/ 1 = 76. Add 76 to the number set. Current number set: [76, 23], target: 44, just two numbers left.\n     |- Try 76 + 23 = 99. Evaluate 99 != 44, drop this branch.\n     |- Try 76 - 23 = 53. Evaluate 53 != 44, drop this branch.\n     |- Try 76 * 23 = 1748. Evaluate 1748 != 44, drop this branch.\n     |- Try 76 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (76, 23) (numbers left: [1]). Try possible operations.\n    |- Try 76 + 23 = 99. Add 99 to the number set. Current number set: [99, 1], target: 44, just two numbers left.\n     |- Try 99 + 1 = 100. Evaluate 100 != 44, drop this branch.\n     |- Try 99 - 1 = 98. Evaluate 98 != 44, drop this branch.\n     |- Try 99 * 1 = 99. Evaluate 99 != 44, drop this branch.\n     |- Try 99 \/ 1 = 99. Evaluate 99 != 44, drop this branch.\n    |- Try 76 - 23 = 53. Add 53 to the number set. Current number set: [53, 1], target: 44, just two numbers left.\n     |- Try 53 + 1 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 53 - 1 = 52. Evaluate 52 != 44, drop this branch.\n     |- Try 53 * 1 = 53. Evaluate 53 != 44, drop this branch.\n     |- Try 53 \/ 1 = 53. Evaluate 53 != 44, drop this branch.\n    |- Try 76 * 23 = 1748. Add 1748 to the number set. Current number set: [1748, 1], target: 44, just two numbers left.\n     |- Try 1748 + 1 = 1749. Evaluate 1749 != 44, drop this branch.\n     |- Try 1748 - 1 = 1747. Evaluate 1747 != 44, drop this branch.\n     |- Try 1748 * 1 = 1748. Evaluate 1748 != 44, drop this branch.\n     |- Try 1748 \/ 1 = 1748. Evaluate 1748 != 44, drop this branch.\n    |- Try 76 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (1, 23) (numbers left: [76]). Try possible operations.\n    |- Try 23 + 1 = 24. Add 24 to the number set. Current number set: [24, 76], target: 44, just two numbers left.\n     |- Try 76 + 24 = 100. Evaluate 100 != 44, drop this branch.\n     |- Try 76 - 24 = 52. Evaluate 52 != 44, drop this branch.\n     |- Try 76 * 24 = 1824. Evaluate 1824 != 44, drop this branch.\n     |- Try 76 \/ 24 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 23 - 1 = 22. Add 22 to the number set. Current number set: [22, 76], target: 44, just two numbers left.\n     |- Try 76 + 22 = 98. Evaluate 98 != 44, drop this branch.\n     |- Try 76 - 22 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 76 * 22 = 1672. Evaluate 1672 != 44, drop this branch.\n     |- Try 76 \/ 22 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 23 * 1 = 23. Add 23 to the number set. Current number set: [23, 76], target: 44, just two numbers left.\n     |- Try 76 + 23 = 99. Evaluate 99 != 44, drop this branch.\n     |- Try 76 - 23 = 53. Evaluate 53 != 44, drop this branch.\n     |- Try 76 * 23 = 1748. Evaluate 1748 != 44, drop this branch.\n     |- Try 76 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 23 \/ 1 = 23. Add 23 to the number set. Current number set: [23, 76], target: 44, just two numbers left.\n     |- Try 76 + 23 = 99. Evaluate 99 != 44, drop this branch.\n     |- Try 76 - 23 = 53. Evaluate 53 != 44, drop this branch.\n     |- Try 76 * 23 = 1748. Evaluate 1748 != 44, drop this branch.\n     |- Try 76 \/ 23 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 48 - 28 = 20. Add 20 to the number set. Current number set: [20, 1, 23], target: 44. Options for choosing two numbers: [(20, 1), (20, 23), (1, 23)].\n   |- Pick two numbers (20, 1) (numbers left: [23]). Try possible operations.\n    |- Try 20 + 1 = 21. Add 21 to the number set. Current number set: [21, 23], target: 44, just two numbers left.\n     |- Try 23 + 21 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 21 = 44\nThe step before: 20 + 1 = 21\nThe first step: 48 - 28 = 20\n\nOutput the solution in the required format:\n<Solution>\n48 - 28 = 20\n20 + 1 = 21\n23 + 21 = 44\n<\/Solution>\n","item":{"nums":[48,28,1,23],"solution":["48 - 28 = 20","20 + 1 = 21","23 + 21 = 44"],"target":44}}
+{"instance_id":"countdown_2k_150","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 10, 28, 2]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [13, 10, 28, 2], target: 27. Options for choosing two numbers: [(13, 10), (13, 28), (13, 2), (10, 28), (10, 2), (28, 2)].\n |- Pick two numbers (13, 10) (numbers left: [28, 2]). Try possible operations.\n  |- Try 13 + 10 = 23. Add 23 to the number set. Current number set: [23, 28, 2], target: 27. Options for choosing two numbers: [(23, 28), (23, 2), (28, 2)].\n   |- Pick two numbers (23, 28) (numbers left: [2]). Try possible operations.\n    |- Try 28 + 23 = 51. Add 51 to the number set. Current number set: [51, 2], target: 27, just two numbers left.\n     |- Try 51 + 2 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 51 - 2 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 51 * 2 = 102. Evaluate 102 != 27, drop this branch.\n     |- Try 51 \/ 2 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 28 - 23 = 5. Add 5 to the number set. Current number set: [5, 2], target: 27, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 27, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 28 * 23 = 644. Add 644 to the number set. Current number set: [644, 2], target: 27, just two numbers left.\n     |- Try 644 + 2 = 646. Evaluate 646 != 27, drop this branch.\n     |- Try 644 - 2 = 642. Evaluate 642 != 27, drop this branch.\n     |- Try 644 * 2 = 1288. Evaluate 1288 != 27, drop this branch.\n     |- Try 644 \/ 2 = 322. Evaluate 322 != 27, drop this branch.\n    |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (23, 2) (numbers left: [28]). Try possible operations.\n    |- Try 23 + 2 = 25. Add 25 to the number set. Current number set: [25, 28], target: 27, just two numbers left.\n     |- Try 28 + 25 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 28 - 25 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 28 * 25 = 700. Evaluate 700 != 27, drop this branch.\n     |- Try 28 \/ 25 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 23 - 2 = 21. Add 21 to the number set. Current number set: [21, 28], target: 27, just two numbers left.\n     |- Try 28 + 21 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 28 - 21 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 28 * 21 = 588. Evaluate 588 != 27, drop this branch.\n     |- Try 28 \/ 21 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 23 * 2 = 46. Add 46 to the number set. Current number set: [46, 28], target: 27, just two numbers left.\n     |- Try 46 + 28 = 74. Evaluate 74 != 27, drop this branch.\n     |- Try 46 - 28 = 18. Evaluate 18 != 27, drop this branch.\n     |- Try 46 * 28 = 1288. Evaluate 1288 != 27, drop this branch.\n     |- Try 46 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 2) (numbers left: [23]). Try possible operations.\n    |- Try 28 + 2 = 30. Add 30 to the number set. Current number set: [30, 23], target: 27, just two numbers left.\n     |- Try 30 + 23 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 30 - 23 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 30 * 23 = 690. Evaluate 690 != 27, drop this branch.\n     |- Try 30 \/ 23 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 28 - 2 = 26. Add 26 to the number set. Current number set: [26, 23], target: 27, just two numbers left.\n     |- Try 26 + 23 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 26 - 23 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 26 * 23 = 598. Evaluate 598 != 27, drop this branch.\n     |- Try 26 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 * 2 = 56. Add 56 to the number set. Current number set: [56, 23], target: 27, just two numbers left.\n     |- Try 56 + 23 = 79. Evaluate 79 != 27, drop this branch.\n     |- Try 56 - 23 = 33. Evaluate 33 != 27, drop this branch.\n     |- Try 56 * 23 = 1288. Evaluate 1288 != 27, drop this branch.\n     |- Try 56 \/ 23 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 28 \/ 2 = 14. Add 14 to the number set. Current number set: [14, 23], target: 27, just two numbers left.\n     |- Try 23 + 14 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 23 - 14 = 9. Evaluate 9 != 27, drop this branch.\n     |- Try 23 * 14 = 322. Evaluate 322 != 27, drop this branch.\n     |- Try 23 \/ 14 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 13 - 10 = 3. Add 3 to the number set. Current number set: [3, 28, 2], target: 27. Options for choosing two numbers: [(3, 28), (3, 2), (28, 2)].\n   |- Pick two numbers (3, 28) (numbers left: [2]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 2], target: 27, just two numbers left.\n     |- Try 31 + 2 = 33. Evaluate 33 != 27, drop this branch.\n     |- Try 31 - 2 = 29. Evaluate 29 != 27, drop this branch.\n     |- Try 31 * 2 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 2], target: 27, just two numbers left.\n     |- Try 25 + 2 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 25 + 2 = 27\nThe step before: 28 - 3 = 25\nThe first step: 13 - 10 = 3\n\nOutput the solution in the required format:\n<Solution>\n13 - 10 = 3\n28 - 3 = 25\n25 + 2 = 27\n<\/Solution>\n","item":{"nums":[13,10,28,2],"solution":["13 - 10 = 3","28 - 3 = 25","25 + 2 = 27"],"target":27}}
+{"instance_id":"countdown_2k_151","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 4, 42, 16]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [18, 4, 42, 16], target: 12. Options for choosing two numbers: [(18, 4), (18, 42), (18, 16), (4, 42), (4, 16), (42, 16)].\n |- Pick two numbers (18, 4) (numbers left: [42, 16]). Try possible operations.\n  |- Try 18 + 4 = 22. Add 22 to the number set. Current number set: [22, 42, 16], target: 12. Options for choosing two numbers: [(22, 42), (22, 16), (42, 16)].\n   |- Pick two numbers (22, 42) (numbers left: [16]). Try possible operations.\n    |- Try 42 + 22 = 64. Add 64 to the number set. Current number set: [64, 16], target: 12, just two numbers left.\n     |- Try 64 + 16 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 64 - 16 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 64 * 16 = 1024. Evaluate 1024 != 12, drop this branch.\n     |- Try 64 \/ 16 = 4. Evaluate 4 != 12, drop this branch.\n    |- Try 42 - 22 = 20. Add 20 to the number set. Current number set: [20, 16], target: 12, just two numbers left.\n     |- Try 20 + 16 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 20 - 16 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 20 * 16 = 320. Evaluate 320 != 12, drop this branch.\n     |- Try 20 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 22 = 924. Add 924 to the number set. Current number set: [924, 16], target: 12, just two numbers left.\n     |- Try 924 + 16 = 940. Evaluate 940 != 12, drop this branch.\n     |- Try 924 - 16 = 908. Evaluate 908 != 12, drop this branch.\n     |- Try 924 * 16 = 14784. 14784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 16 = 57.8. 57.8 is a decimal, drop this branch.\n    |- Try 42 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (22, 16) (numbers left: [42]). Try possible operations.\n    |- Try 22 + 16 = 38. Add 38 to the number set. Current number set: [38, 42], target: 12, just two numbers left.\n     |- Try 42 + 38 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 42 - 38 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 42 * 38 = 1596. Evaluate 1596 != 12, drop this branch.\n     |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 - 16 = 6. Add 6 to the number set. Current number set: [6, 42], target: 12, just two numbers left.\n     |- Try 42 + 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 42 - 6 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 42 * 6 = 252. Evaluate 252 != 12, drop this branch.\n     |- Try 42 \/ 6 = 7. Evaluate 7 != 12, drop this branch.\n    |- Try 22 * 16 = 352. Add 352 to the number set. Current number set: [352, 42], target: 12, just two numbers left.\n     |- Try 352 + 42 = 394. Evaluate 394 != 12, drop this branch.\n     |- Try 352 - 42 = 310. Evaluate 310 != 12, drop this branch.\n     |- Try 352 * 42 = 14784. 14784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 42 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 16) (numbers left: [22]). Try possible operations.\n    |- Try 42 + 16 = 58. Add 58 to the number set. Current number set: [58, 22], target: 12, just two numbers left.\n     |- Try 58 + 22 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 58 - 22 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 58 * 22 = 1276. Evaluate 1276 != 12, drop this branch.\n     |- Try 58 \/ 22 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 42 - 16 = 26. Add 26 to the number set. Current number set: [26, 22], target: 12, just two numbers left.\n     |- Try 26 + 22 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 26 - 22 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 26 * 22 = 572. Evaluate 572 != 12, drop this branch.\n     |- Try 26 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 16 = 672. Add 672 to the number set. Current number set: [672, 22], target: 12, just two numbers left.\n     |- Try 672 + 22 = 694. Evaluate 694 != 12, drop this branch.\n     |- Try 672 - 22 = 650. Evaluate 650 != 12, drop this branch.\n     |- Try 672 * 22 = 14784. 14784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 672 \/ 22 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 42 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 18 - 4 = 14. Add 14 to the number set. Current number set: [14, 42, 16], target: 12. Options for choosing two numbers: [(14, 42), (14, 16), (42, 16)].\n   |- Pick two numbers (14, 42) (numbers left: [16]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 16], target: 12, just two numbers left.\n     |- Try 56 + 16 = 72. Evaluate 72 != 12, drop this branch.\n     |- Try 56 - 16 = 40. Evaluate 40 != 12, drop this branch.\n     |- Try 56 * 16 = 896. Evaluate 896 != 12, drop this branch.\n     |- Try 56 \/ 16 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 16], target: 12, just two numbers left.\n     |- Try 28 + 16 = 44. Evaluate 44 != 12, drop this branch.\n     |- Try 28 - 16 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 - 16 = 12\nThe step before: 42 - 14 = 28\nThe first step: 18 - 4 = 14\n\nOutput the solution in the required format:\n<Solution>\n18 - 4 = 14\n42 - 14 = 28\n28 - 16 = 12\n<\/Solution>\n","item":{"nums":[18,4,42,16],"solution":["18 - 4 = 14","42 - 14 = 28","28 - 16 = 12"],"target":12}}
+{"instance_id":"countdown_2k_152","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 49, 26, 10]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [41, 49, 26, 10], target: 44. Options for choosing two numbers: [(41, 49), (41, 26), (41, 10), (49, 26), (49, 10), (26, 10)].\n |- Pick two numbers (41, 49) (numbers left: [26, 10]). Try possible operations.\n  |- Try 49 + 41 = 90. Add 90 to the number set. Current number set: [90, 26, 10], target: 44. Options for choosing two numbers: [(90, 26), (90, 10), (26, 10)].\n   |- Pick two numbers (90, 26) (numbers left: [10]). Try possible operations.\n    |- Try 90 + 26 = 116. Add 116 to the number set. Current number set: [116, 10], target: 44, just two numbers left.\n     |- Try 116 + 10 = 126. Evaluate 126 != 44, drop this branch.\n     |- Try 116 - 10 = 106. Evaluate 106 != 44, drop this branch.\n     |- Try 116 * 10 = 1160. Evaluate 1160 != 44, drop this branch.\n     |- Try 116 \/ 10 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 90 - 26 = 64. Add 64 to the number set. Current number set: [64, 10], target: 44, just two numbers left.\n     |- Try 64 + 10 = 74. Evaluate 74 != 44, drop this branch.\n     |- Try 64 - 10 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 64 * 10 = 640. Evaluate 640 != 44, drop this branch.\n     |- Try 64 \/ 10 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 90 * 26 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n    |- Try 90 \/ 26 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (90, 10) (numbers left: [26]). Try possible operations.\n    |- Try 90 + 10 = 100. Add 100 to the number set. Current number set: [100, 26], target: 44, just two numbers left.\n     |- Try 100 + 26 = 126. Evaluate 126 != 44, drop this branch.\n     |- Try 100 - 26 = 74. Evaluate 74 != 44, drop this branch.\n     |- Try 100 * 26 = 2600. 2600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 26 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 90 - 10 = 80. Add 80 to the number set. Current number set: [80, 26], target: 44, just two numbers left.\n     |- Try 80 + 26 = 106. Evaluate 106 != 44, drop this branch.\n     |- Try 80 - 26 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 80 * 26 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 26 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 90 * 10 = 900. Add 900 to the number set. Current number set: [900, 26], target: 44, just two numbers left.\n     |- Try 900 + 26 = 926. Evaluate 926 != 44, drop this branch.\n     |- Try 900 - 26 = 874. Evaluate 874 != 44, drop this branch.\n     |- Try 900 * 26 = 23400. 23400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 900 \/ 26 = 34.6. 34.6 is a decimal, drop this branch.\n    |- Try 90 \/ 10 = 9. Add 9 to the number set. Current number set: [9, 26], target: 44, just two numbers left.\n     |- Try 26 + 9 = 35. Evaluate 35 != 44, drop this branch.\n     |- Try 26 - 9 = 17. Evaluate 17 != 44, drop this branch.\n     |- Try 26 * 9 = 234. Evaluate 234 != 44, drop this branch.\n     |- Try 26 \/ 9 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (26, 10) (numbers left: [90]). Try possible operations.\n    |- Try 26 + 10 = 36. Add 36 to the number set. Current number set: [36, 90], target: 44, just two numbers left.\n     |- Try 90 + 36 = 126. Evaluate 126 != 44, drop this branch.\n     |- Try 90 - 36 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 90 * 36 = 3240. 3240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 36 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 26 - 10 = 16. Add 16 to the number set. Current number set: [16, 90], target: 44, just two numbers left.\n     |- Try 90 + 16 = 106. Evaluate 106 != 44, drop this branch.\n     |- Try 90 - 16 = 74. Evaluate 74 != 44, drop this branch.\n     |- Try 90 * 16 = 1440. Evaluate 1440 != 44, drop this branch.\n     |- Try 90 \/ 16 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 26 * 10 = 260. Add 260 to the number set. Current number set: [260, 90], target: 44, just two numbers left.\n     |- Try 260 + 90 = 350. Evaluate 350 != 44, drop this branch.\n     |- Try 260 - 90 = 170. Evaluate 170 != 44, drop this branch.\n     |- Try 260 * 90 = 23400. 23400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 260 \/ 90 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 26 \/ 10 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 49 - 41 = 8. Add 8 to the number set. Current number set: [8, 26, 10], target: 44. Options for choosing two numbers: [(8, 26), (8, 10), (26, 10)].\n   |- Pick two numbers (8, 26) (numbers left: [10]). Try possible operations.\n    |- Try 26 + 8 = 34. Add 34 to the number set. Current number set: [34, 10], target: 44, just two numbers left.\n     |- Try 34 + 10 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 10 = 44\nThe step before: 26 + 8 = 34\nThe first step: 49 - 41 = 8\n\nOutput the solution in the required format:\n<Solution>\n49 - 41 = 8\n26 + 8 = 34\n34 + 10 = 44\n<\/Solution>\n","item":{"nums":[41,49,26,10],"solution":["49 - 41 = 8","26 + 8 = 34","34 + 10 = 44"],"target":44}}
+{"instance_id":"countdown_2k_153","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 12, 30, 12]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [32, 12, 30, 12], target: 38. Options for choosing two numbers: [(32, 12), (32, 30), (32, 12), (12, 30), (12, 12), (30, 12)].\n |- Pick two numbers (32, 12) (numbers left: [30, 12]). Try possible operations.\n  |- Try 32 + 12 = 44. Add 44 to the number set. Current number set: [44, 30, 12], target: 38. Options for choosing two numbers: [(44, 30), (44, 12), (30, 12)].\n   |- Pick two numbers (44, 30) (numbers left: [12]). Try possible operations.\n    |- Try 44 + 30 = 74. Add 74 to the number set. Current number set: [74, 12], target: 38, just two numbers left.\n     |- Try 74 + 12 = 86. Evaluate 86 != 38, drop this branch.\n     |- Try 74 - 12 = 62. Evaluate 62 != 38, drop this branch.\n     |- Try 74 * 12 = 888. Evaluate 888 != 38, drop this branch.\n     |- Try 74 \/ 12 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 44 - 30 = 14. Add 14 to the number set. Current number set: [14, 12], target: 38, just two numbers left.\n     |- Try 14 + 12 = 26. Evaluate 26 != 38, drop this branch.\n     |- Try 14 - 12 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 14 * 12 = 168. Evaluate 168 != 38, drop this branch.\n     |- Try 14 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 30 = 1320. Add 1320 to the number set. Current number set: [1320, 12], target: 38, just two numbers left.\n     |- Try 1320 + 12 = 1332. Evaluate 1332 != 38, drop this branch.\n     |- Try 1320 - 12 = 1308. Evaluate 1308 != 38, drop this branch.\n     |- Try 1320 * 12 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1320 \/ 12 = 110. Evaluate 110 != 38, drop this branch.\n    |- Try 44 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (44, 12) (numbers left: [30]). Try possible operations.\n    |- Try 44 + 12 = 56. Add 56 to the number set. Current number set: [56, 30], target: 38, just two numbers left.\n     |- Try 56 + 30 = 86. Evaluate 86 != 38, drop this branch.\n     |- Try 56 - 30 = 26. Evaluate 26 != 38, drop this branch.\n     |- Try 56 * 30 = 1680. Evaluate 1680 != 38, drop this branch.\n     |- Try 56 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 - 12 = 32. Add 32 to the number set. Current number set: [32, 30], target: 38, just two numbers left.\n     |- Try 32 + 30 = 62. Evaluate 62 != 38, drop this branch.\n     |- Try 32 - 30 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 32 * 30 = 960. Evaluate 960 != 38, drop this branch.\n     |- Try 32 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 12 = 528. Add 528 to the number set. Current number set: [528, 30], target: 38, just two numbers left.\n     |- Try 528 + 30 = 558. Evaluate 558 != 38, drop this branch.\n     |- Try 528 - 30 = 498. Evaluate 498 != 38, drop this branch.\n     |- Try 528 * 30 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 30 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (30, 12) (numbers left: [44]). Try possible operations.\n    |- Try 30 + 12 = 42. Add 42 to the number set. Current number set: [42, 44], target: 38, just two numbers left.\n     |- Try 44 + 42 = 86. Evaluate 86 != 38, drop this branch.\n     |- Try 44 - 42 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 44 * 42 = 1848. Evaluate 1848 != 38, drop this branch.\n     |- Try 44 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 - 12 = 18. Add 18 to the number set. Current number set: [18, 44], target: 38, just two numbers left.\n     |- Try 44 + 18 = 62. Evaluate 62 != 38, drop this branch.\n     |- Try 44 - 18 = 26. Evaluate 26 != 38, drop this branch.\n     |- Try 44 * 18 = 792. Evaluate 792 != 38, drop this branch.\n     |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 30 * 12 = 360. Add 360 to the number set. Current number set: [360, 44], target: 38, just two numbers left.\n     |- Try 360 + 44 = 404. Evaluate 404 != 38, drop this branch.\n     |- Try 360 - 44 = 316. Evaluate 316 != 38, drop this branch.\n     |- Try 360 * 44 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 44 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 30 \/ 12 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 32 - 12 = 20. Add 20 to the number set. Current number set: [20, 30, 12], target: 38. Options for choosing two numbers: [(20, 30), (20, 12), (30, 12)].\n   |- Pick two numbers (20, 30) (numbers left: [12]). Try possible operations.\n    |- Try 30 + 20 = 50. Add 50 to the number set. Current number set: [50, 12], target: 38, just two numbers left.\n     |- Try 50 + 12 = 62. Evaluate 62 != 38, drop this branch.\n     |- Try 50 - 12 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 50 - 12 = 38\nThe step before: 30 + 20 = 50\nThe first step: 32 - 12 = 20\n\nOutput the solution in the required format:\n<Solution>\n32 - 12 = 20\n30 + 20 = 50\n50 - 12 = 38\n<\/Solution>\n","item":{"nums":[32,12,30,12],"solution":["32 - 12 = 20","30 + 20 = 50","50 - 12 = 38"],"target":38}}
+{"instance_id":"countdown_2k_154","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 42, 26, 7]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [30, 42, 26, 7], target: 21. Options for choosing two numbers: [(30, 42), (30, 26), (30, 7), (42, 26), (42, 7), (26, 7)].\n |- Pick two numbers (30, 42) (numbers left: [26, 7]). Try possible operations.\n  |- Try 42 + 30 = 72. Add 72 to the number set. Current number set: [72, 26, 7], target: 21. Options for choosing two numbers: [(72, 26), (72, 7), (26, 7)].\n   |- Pick two numbers (72, 26) (numbers left: [7]). Try possible operations.\n    |- Try 72 + 26 = 98. Add 98 to the number set. Current number set: [98, 7], target: 21, just two numbers left.\n     |- Try 98 + 7 = 105. Evaluate 105 != 21, drop this branch.\n     |- Try 98 - 7 = 91. Evaluate 91 != 21, drop this branch.\n     |- Try 98 * 7 = 686. Evaluate 686 != 21, drop this branch.\n     |- Try 98 \/ 7 = 14. Evaluate 14 != 21, drop this branch.\n    |- Try 72 - 26 = 46. Add 46 to the number set. Current number set: [46, 7], target: 21, just two numbers left.\n     |- Try 46 + 7 = 53. Evaluate 53 != 21, drop this branch.\n     |- Try 46 - 7 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 46 * 7 = 322. Evaluate 322 != 21, drop this branch.\n     |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 72 * 26 = 1872. Add 1872 to the number set. Current number set: [1872, 7], target: 21, just two numbers left.\n     |- Try 1872 + 7 = 1879. Evaluate 1879 != 21, drop this branch.\n     |- Try 1872 - 7 = 1865. Evaluate 1865 != 21, drop this branch.\n     |- Try 1872 * 7 = 13104. 13104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 7 = 267.4. 267.4 is a decimal, drop this branch.\n    |- Try 72 \/ 26 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (72, 7) (numbers left: [26]). Try possible operations.\n    |- Try 72 + 7 = 79. Add 79 to the number set. Current number set: [79, 26], target: 21, just two numbers left.\n     |- Try 79 + 26 = 105. Evaluate 105 != 21, drop this branch.\n     |- Try 79 - 26 = 53. Evaluate 53 != 21, drop this branch.\n     |- Try 79 * 26 = 2054. 2054 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 26 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 72 - 7 = 65. Add 65 to the number set. Current number set: [65, 26], target: 21, just two numbers left.\n     |- Try 65 + 26 = 91. Evaluate 91 != 21, drop this branch.\n     |- Try 65 - 26 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 65 * 26 = 1690. Evaluate 1690 != 21, drop this branch.\n     |- Try 65 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 72 * 7 = 504. Add 504 to the number set. Current number set: [504, 26], target: 21, just two numbers left.\n     |- Try 504 + 26 = 530. Evaluate 530 != 21, drop this branch.\n     |- Try 504 - 26 = 478. Evaluate 478 != 21, drop this branch.\n     |- Try 504 * 26 = 13104. 13104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 504 \/ 26 = 19.4. 19.4 is a decimal, drop this branch.\n    |- Try 72 \/ 7 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (26, 7) (numbers left: [72]). Try possible operations.\n    |- Try 26 + 7 = 33. Add 33 to the number set. Current number set: [33, 72], target: 21, just two numbers left.\n     |- Try 72 + 33 = 105. Evaluate 105 != 21, drop this branch.\n     |- Try 72 - 33 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 72 * 33 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 26 - 7 = 19. Add 19 to the number set. Current number set: [19, 72], target: 21, just two numbers left.\n     |- Try 72 + 19 = 91. Evaluate 91 != 21, drop this branch.\n     |- Try 72 - 19 = 53. Evaluate 53 != 21, drop this branch.\n     |- Try 72 * 19 = 1368. Evaluate 1368 != 21, drop this branch.\n     |- Try 72 \/ 19 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 26 * 7 = 182. Add 182 to the number set. Current number set: [182, 72], target: 21, just two numbers left.\n     |- Try 182 + 72 = 254. Evaluate 254 != 21, drop this branch.\n     |- Try 182 - 72 = 110. Evaluate 110 != 21, drop this branch.\n     |- Try 182 * 72 = 13104. 13104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 182 \/ 72 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 42 - 30 = 12. Add 12 to the number set. Current number set: [12, 26, 7], target: 21. Options for choosing two numbers: [(12, 26), (12, 7), (26, 7)].\n   |- Pick two numbers (12, 26) (numbers left: [7]). Try possible operations.\n    |- Try 26 + 12 = 38. Add 38 to the number set. Current number set: [38, 7], target: 21, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 21, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 21, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 26 - 12 = 14. Add 14 to the number set. Current number set: [14, 7], target: 21, just two numbers left.\n     |- Try 14 + 7 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 14 + 7 = 21\nThe step before: 26 - 12 = 14\nThe first step: 42 - 30 = 12\n\nOutput the solution in the required format:\n<Solution>\n42 - 30 = 12\n26 - 12 = 14\n14 + 7 = 21\n<\/Solution>\n","item":{"nums":[30,42,26,7],"solution":["42 - 30 = 12","26 - 12 = 14","14 + 7 = 21"],"target":21}}
+{"instance_id":"countdown_2k_155","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [40, 22, 8, 24]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [40, 22, 8, 24], target: 14. Options for choosing two numbers: [(40, 22), (40, 8), (40, 24), (22, 8), (22, 24), (8, 24)].\n |- Pick two numbers (40, 22) (numbers left: [8, 24]). Try possible operations.\n  |- Try 40 + 22 = 62. Add 62 to the number set. Current number set: [62, 8, 24], target: 14. Options for choosing two numbers: [(62, 8), (62, 24), (8, 24)].\n   |- Pick two numbers (62, 8) (numbers left: [24]). Try possible operations.\n    |- Try 62 + 8 = 70. Add 70 to the number set. Current number set: [70, 24], target: 14, just two numbers left.\n     |- Try 70 + 24 = 94. Evaluate 94 != 14, drop this branch.\n     |- Try 70 - 24 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 70 * 24 = 1680. Evaluate 1680 != 14, drop this branch.\n     |- Try 70 \/ 24 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 62 - 8 = 54. Add 54 to the number set. Current number set: [54, 24], target: 14, just two numbers left.\n     |- Try 54 + 24 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 54 - 24 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 54 * 24 = 1296. Evaluate 1296 != 14, drop this branch.\n     |- Try 54 \/ 24 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 62 * 8 = 496. Add 496 to the number set. Current number set: [496, 24], target: 14, just two numbers left.\n     |- Try 496 + 24 = 520. Evaluate 520 != 14, drop this branch.\n     |- Try 496 - 24 = 472. Evaluate 472 != 14, drop this branch.\n     |- Try 496 * 24 = 11904. 11904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 496 \/ 24 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 62 \/ 8 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (62, 24) (numbers left: [8]). Try possible operations.\n    |- Try 62 + 24 = 86. Add 86 to the number set. Current number set: [86, 8], target: 14, just two numbers left.\n     |- Try 86 + 8 = 94. Evaluate 94 != 14, drop this branch.\n     |- Try 86 - 8 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 86 * 8 = 688. Evaluate 688 != 14, drop this branch.\n     |- Try 86 \/ 8 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 62 - 24 = 38. Add 38 to the number set. Current number set: [38, 8], target: 14, just two numbers left.\n     |- Try 38 + 8 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 38 - 8 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 38 * 8 = 304. Evaluate 304 != 14, drop this branch.\n     |- Try 38 \/ 8 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 62 * 24 = 1488. Add 1488 to the number set. Current number set: [1488, 8], target: 14, just two numbers left.\n     |- Try 1488 + 8 = 1496. Evaluate 1496 != 14, drop this branch.\n     |- Try 1488 - 8 = 1480. Evaluate 1480 != 14, drop this branch.\n     |- Try 1488 * 8 = 11904. 11904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1488 \/ 8 = 186. Evaluate 186 != 14, drop this branch.\n    |- Try 62 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 24) (numbers left: [62]). Try possible operations.\n    |- Try 24 + 8 = 32. Add 32 to the number set. Current number set: [32, 62], target: 14, just two numbers left.\n     |- Try 62 + 32 = 94. Evaluate 94 != 14, drop this branch.\n     |- Try 62 - 32 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 62 * 32 = 1984. Evaluate 1984 != 14, drop this branch.\n     |- Try 62 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 24 - 8 = 16. Add 16 to the number set. Current number set: [16, 62], target: 14, just two numbers left.\n     |- Try 62 + 16 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 62 - 16 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 62 * 16 = 992. Evaluate 992 != 14, drop this branch.\n     |- Try 62 \/ 16 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 24 * 8 = 192. Add 192 to the number set. Current number set: [192, 62], target: 14, just two numbers left.\n     |- Try 192 + 62 = 254. Evaluate 254 != 14, drop this branch.\n     |- Try 192 - 62 = 130. Evaluate 130 != 14, drop this branch.\n     |- Try 192 * 62 = 11904. 11904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 62 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 24 \/ 8 = 3. Add 3 to the number set. Current number set: [3, 62], target: 14, just two numbers left.\n     |- Try 62 + 3 = 65. Evaluate 65 != 14, drop this branch.\n     |- Try 62 - 3 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 62 * 3 = 186. Evaluate 186 != 14, drop this branch.\n     |- Try 62 \/ 3 = 20.7. 20.7 is a decimal, drop this branch.\n  |- Try 40 - 22 = 18. Add 18 to the number set. Current number set: [18, 8, 24], target: 14. Options for choosing two numbers: [(18, 8), (18, 24), (8, 24)].\n   |- Pick two numbers (18, 8) (numbers left: [24]). Try possible operations.\n    |- Try 18 + 8 = 26. Add 26 to the number set. Current number set: [26, 24], target: 14, just two numbers left.\n     |- Try 26 + 24 = 50. Evaluate 50 != 14, drop this branch.\n     |- Try 26 - 24 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 26 * 24 = 624. Evaluate 624 != 14, drop this branch.\n     |- Try 26 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 18 - 8 = 10. Add 10 to the number set. Current number set: [10, 24], target: 14, just two numbers left.\n     |- Try 24 + 10 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 24 - 10 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 - 10 = 14\nThe step before: 18 - 8 = 10\nThe first step: 40 - 22 = 18\n\nOutput the solution in the required format:\n<Solution>\n40 - 22 = 18\n18 - 8 = 10\n24 - 10 = 14\n<\/Solution>\n","item":{"nums":[40,22,8,24],"solution":["40 - 22 = 18","18 - 8 = 10","24 - 10 = 14"],"target":14}}
+{"instance_id":"countdown_2k_156","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 28, 10, 43]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [44, 28, 10, 43], target: 37. Options for choosing two numbers: [(44, 28), (44, 10), (44, 43), (28, 10), (28, 43), (10, 43)].\n |- Pick two numbers (44, 28) (numbers left: [10, 43]). Try possible operations.\n  |- Try 44 + 28 = 72. Add 72 to the number set. Current number set: [72, 10, 43], target: 37. Options for choosing two numbers: [(72, 10), (72, 43), (10, 43)].\n   |- Pick two numbers (72, 10) (numbers left: [43]). Try possible operations.\n    |- Try 72 + 10 = 82. Add 82 to the number set. Current number set: [82, 43], target: 37, just two numbers left.\n     |- Try 82 + 43 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 82 - 43 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 82 * 43 = 3526. 3526 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 43 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 72 - 10 = 62. Add 62 to the number set. Current number set: [62, 43], target: 37, just two numbers left.\n     |- Try 62 + 43 = 105. Evaluate 105 != 37, drop this branch.\n     |- Try 62 - 43 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 62 * 43 = 2666. 2666 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 43 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 72 * 10 = 720. Add 720 to the number set. Current number set: [720, 43], target: 37, just two numbers left.\n     |- Try 720 + 43 = 763. Evaluate 763 != 37, drop this branch.\n     |- Try 720 - 43 = 677. Evaluate 677 != 37, drop this branch.\n     |- Try 720 * 43 = 30960. 30960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 43 = 16.7. 16.7 is a decimal, drop this branch.\n    |- Try 72 \/ 10 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (72, 43) (numbers left: [10]). Try possible operations.\n    |- Try 72 + 43 = 115. Add 115 to the number set. Current number set: [115, 10], target: 37, just two numbers left.\n     |- Try 115 + 10 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 115 - 10 = 105. Evaluate 105 != 37, drop this branch.\n     |- Try 115 * 10 = 1150. Evaluate 1150 != 37, drop this branch.\n     |- Try 115 \/ 10 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 72 - 43 = 29. Add 29 to the number set. Current number set: [29, 10], target: 37, just two numbers left.\n     |- Try 29 + 10 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 29 - 10 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 29 * 10 = 290. Evaluate 290 != 37, drop this branch.\n     |- Try 29 \/ 10 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 72 * 43 = 3096. 3096 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 43 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 43) (numbers left: [72]). Try possible operations.\n    |- Try 43 + 10 = 53. Add 53 to the number set. Current number set: [53, 72], target: 37, just two numbers left.\n     |- Try 72 + 53 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 72 - 53 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 72 * 53 = 3816. 3816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 53 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 43 - 10 = 33. Add 33 to the number set. Current number set: [33, 72], target: 37, just two numbers left.\n     |- Try 72 + 33 = 105. Evaluate 105 != 37, drop this branch.\n     |- Try 72 - 33 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 72 * 33 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 43 * 10 = 430. Add 430 to the number set. Current number set: [430, 72], target: 37, just two numbers left.\n     |- Try 430 + 72 = 502. Evaluate 502 != 37, drop this branch.\n     |- Try 430 - 72 = 358. Evaluate 358 != 37, drop this branch.\n     |- Try 430 * 72 = 30960. 30960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 430 \/ 72 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 43 \/ 10 = 4.3. 4.3 is a decimal, drop this branch.\n  |- Try 44 - 28 = 16. Add 16 to the number set. Current number set: [16, 10, 43], target: 37. Options for choosing two numbers: [(16, 10), (16, 43), (10, 43)].\n   |- Pick two numbers (16, 10) (numbers left: [43]). Try possible operations.\n    |- Try 16 + 10 = 26. Add 26 to the number set. Current number set: [26, 43], target: 37, just two numbers left.\n     |- Try 43 + 26 = 69. Evaluate 69 != 37, drop this branch.\n     |- Try 43 - 26 = 17. Evaluate 17 != 37, drop this branch.\n     |- Try 43 * 26 = 1118. Evaluate 1118 != 37, drop this branch.\n     |- Try 43 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 16 - 10 = 6. Add 6 to the number set. Current number set: [6, 43], target: 37, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 - 6 = 37\nThe step before: 16 - 10 = 6\nThe first step: 44 - 28 = 16\n\nOutput the solution in the required format:\n<Solution>\n44 - 28 = 16\n16 - 10 = 6\n43 - 6 = 37\n<\/Solution>\n","item":{"nums":[44,28,10,43],"solution":["44 - 28 = 16","16 - 10 = 6","43 - 6 = 37"],"target":37}}
+{"instance_id":"countdown_2k_157","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [28, 31, 45, 27]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [28, 31, 45, 27], target: 21. Options for choosing two numbers: [(28, 31), (28, 45), (28, 27), (31, 45), (31, 27), (45, 27)].\n |- Pick two numbers (28, 31) (numbers left: [45, 27]). Try possible operations.\n  |- Try 31 + 28 = 59. Add 59 to the number set. Current number set: [59, 45, 27], target: 21. Options for choosing two numbers: [(59, 45), (59, 27), (45, 27)].\n   |- Pick two numbers (59, 45) (numbers left: [27]). Try possible operations.\n    |- Try 59 + 45 = 104. Add 104 to the number set. Current number set: [104, 27], target: 21, just two numbers left.\n     |- Try 104 + 27 = 131. Evaluate 131 != 21, drop this branch.\n     |- Try 104 - 27 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 104 * 27 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 27 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 59 - 45 = 14. Add 14 to the number set. Current number set: [14, 27], target: 21, just two numbers left.\n     |- Try 27 + 14 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 27 - 14 = 13. Evaluate 13 != 21, drop this branch.\n     |- Try 27 * 14 = 378. Evaluate 378 != 21, drop this branch.\n     |- Try 27 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 59 * 45 = 2655. 2655 exceeds the maximum intermediate result, drop this branch.\n    |- Try 59 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (59, 27) (numbers left: [45]). Try possible operations.\n    |- Try 59 + 27 = 86. Add 86 to the number set. Current number set: [86, 45], target: 21, just two numbers left.\n     |- Try 86 + 45 = 131. Evaluate 131 != 21, drop this branch.\n     |- Try 86 - 45 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 86 * 45 = 3870. 3870 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 45 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 59 - 27 = 32. Add 32 to the number set. Current number set: [32, 45], target: 21, just two numbers left.\n     |- Try 45 + 32 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 45 - 32 = 13. Evaluate 13 != 21, drop this branch.\n     |- Try 45 * 32 = 1440. Evaluate 1440 != 21, drop this branch.\n     |- Try 45 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 59 * 27 = 1593. Add 1593 to the number set. Current number set: [1593, 45], target: 21, just two numbers left.\n     |- Try 1593 + 45 = 1638. Evaluate 1638 != 21, drop this branch.\n     |- Try 1593 - 45 = 1548. Evaluate 1548 != 21, drop this branch.\n     |- Try 1593 * 45 = 71685. 71685 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1593 \/ 45 = 35.4. 35.4 is a decimal, drop this branch.\n    |- Try 59 \/ 27 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (45, 27) (numbers left: [59]). Try possible operations.\n    |- Try 45 + 27 = 72. Add 72 to the number set. Current number set: [72, 59], target: 21, just two numbers left.\n     |- Try 72 + 59 = 131. Evaluate 131 != 21, drop this branch.\n     |- Try 72 - 59 = 13. Evaluate 13 != 21, drop this branch.\n     |- Try 72 * 59 = 4248. 4248 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 59 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 - 27 = 18. Add 18 to the number set. Current number set: [18, 59], target: 21, just two numbers left.\n     |- Try 59 + 18 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 59 - 18 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 59 * 18 = 1062. Evaluate 1062 != 21, drop this branch.\n     |- Try 59 \/ 18 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 45 * 27 = 1215. Add 1215 to the number set. Current number set: [1215, 59], target: 21, just two numbers left.\n     |- Try 1215 + 59 = 1274. Evaluate 1274 != 21, drop this branch.\n     |- Try 1215 - 59 = 1156. Evaluate 1156 != 21, drop this branch.\n     |- Try 1215 * 59 = 71685. 71685 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1215 \/ 59 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 45 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 31 - 28 = 3. Add 3 to the number set. Current number set: [3, 45, 27], target: 21. Options for choosing two numbers: [(3, 45), (3, 27), (45, 27)].\n   |- Pick two numbers (3, 45) (numbers left: [27]). Try possible operations.\n    |- Try 45 + 3 = 48. Add 48 to the number set. Current number set: [48, 27], target: 21, just two numbers left.\n     |- Try 48 + 27 = 75. Evaluate 75 != 21, drop this branch.\n     |- Try 48 - 27 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 27 = 21\nThe step before: 45 + 3 = 48\nThe first step: 31 - 28 = 3\n\nOutput the solution in the required format:\n<Solution>\n31 - 28 = 3\n45 + 3 = 48\n48 - 27 = 21\n<\/Solution>\n","item":{"nums":[28,31,45,27],"solution":["31 - 28 = 3","45 + 3 = 48","48 - 27 = 21"],"target":21}}
+{"instance_id":"countdown_2k_158","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 14, 2, 24]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [1, 14, 2, 24], target: 33. Options for choosing two numbers: [(1, 14), (1, 2), (1, 24), (14, 2), (14, 24), (2, 24)].\n |- Pick two numbers (1, 14) (numbers left: [2, 24]). Try possible operations.\n  |- Try 14 + 1 = 15. Add 15 to the number set. Current number set: [15, 2, 24], target: 33. Options for choosing two numbers: [(15, 2), (15, 24), (2, 24)].\n   |- Pick two numbers (15, 2) (numbers left: [24]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 24], target: 33, just two numbers left.\n     |- Try 24 + 17 = 41. Evaluate 41 != 33, drop this branch.\n     |- Try 24 - 17 = 7. Evaluate 7 != 33, drop this branch.\n     |- Try 24 * 17 = 408. Evaluate 408 != 33, drop this branch.\n     |- Try 24 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 24], target: 33, just two numbers left.\n     |- Try 24 + 13 = 37. Evaluate 37 != 33, drop this branch.\n     |- Try 24 - 13 = 11. Evaluate 11 != 33, drop this branch.\n     |- Try 24 * 13 = 312. Evaluate 312 != 33, drop this branch.\n     |- Try 24 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 15 * 2 = 30. Add 30 to the number set. Current number set: [30, 24], target: 33, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 33, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 33, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (15, 24) (numbers left: [2]). Try possible operations.\n    |- Try 24 + 15 = 39. Add 39 to the number set. Current number set: [39, 2], target: 33, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 33, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 33, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 33, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 24 - 15 = 9. Add 9 to the number set. Current number set: [9, 2], target: 33, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 33, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 33, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 24 * 15 = 360. Add 360 to the number set. Current number set: [360, 2], target: 33, just two numbers left.\n     |- Try 360 + 2 = 362. Evaluate 362 != 33, drop this branch.\n     |- Try 360 - 2 = 358. Evaluate 358 != 33, drop this branch.\n     |- Try 360 * 2 = 720. Evaluate 720 != 33, drop this branch.\n     |- Try 360 \/ 2 = 180. Evaluate 180 != 33, drop this branch.\n    |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (2, 24) (numbers left: [15]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 15], target: 33, just two numbers left.\n     |- Try 26 + 15 = 41. Evaluate 41 != 33, drop this branch.\n     |- Try 26 - 15 = 11. Evaluate 11 != 33, drop this branch.\n     |- Try 26 * 15 = 390. Evaluate 390 != 33, drop this branch.\n     |- Try 26 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 15], target: 33, just two numbers left.\n     |- Try 22 + 15 = 37. Evaluate 37 != 33, drop this branch.\n     |- Try 22 - 15 = 7. Evaluate 7 != 33, drop this branch.\n     |- Try 22 * 15 = 330. Evaluate 330 != 33, drop this branch.\n     |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 15], target: 33, just two numbers left.\n     |- Try 48 + 15 = 63. Evaluate 63 != 33, drop this branch.\n     |- Try 48 - 15 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 15 = 33\nThe step before: 24 * 2 = 48\nThe first step: 14 + 1 = 15\n\nOutput the solution in the required format:\n<Solution>\n14 + 1 = 15\n24 * 2 = 48\n48 - 15 = 33\n<\/Solution>\n","item":{"nums":[1,14,2,24],"solution":["14 + 1 = 15","24 * 2 = 48","48 - 15 = 33"],"target":33}}
+{"instance_id":"countdown_2k_159","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 27, 47, 22]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [31, 27, 47, 22], target: 29. Options for choosing two numbers: [(31, 27), (31, 47), (31, 22), (27, 47), (27, 22), (47, 22)].\n |- Pick two numbers (31, 27) (numbers left: [47, 22]). Try possible operations.\n  |- Try 31 + 27 = 58. Add 58 to the number set. Current number set: [58, 47, 22], target: 29. Options for choosing two numbers: [(58, 47), (58, 22), (47, 22)].\n   |- Pick two numbers (58, 47) (numbers left: [22]). Try possible operations.\n    |- Try 58 + 47 = 105. Add 105 to the number set. Current number set: [105, 22], target: 29, just two numbers left.\n     |- Try 105 + 22 = 127. Evaluate 127 != 29, drop this branch.\n     |- Try 105 - 22 = 83. Evaluate 83 != 29, drop this branch.\n     |- Try 105 * 22 = 2310. 2310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 22 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 58 - 47 = 11. Add 11 to the number set. Current number set: [11, 22], target: 29, just two numbers left.\n     |- Try 22 + 11 = 33. Evaluate 33 != 29, drop this branch.\n     |- Try 22 - 11 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 22 * 11 = 242. Evaluate 242 != 29, drop this branch.\n     |- Try 22 \/ 11 = 2. Evaluate 2 != 29, drop this branch.\n    |- Try 58 * 47 = 2726. 2726 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (58, 22) (numbers left: [47]). Try possible operations.\n    |- Try 58 + 22 = 80. Add 80 to the number set. Current number set: [80, 47], target: 29, just two numbers left.\n     |- Try 80 + 47 = 127. Evaluate 127 != 29, drop this branch.\n     |- Try 80 - 47 = 33. Evaluate 33 != 29, drop this branch.\n     |- Try 80 * 47 = 3760. 3760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 47 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 58 - 22 = 36. Add 36 to the number set. Current number set: [36, 47], target: 29, just two numbers left.\n     |- Try 47 + 36 = 83. Evaluate 83 != 29, drop this branch.\n     |- Try 47 - 36 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 47 * 36 = 1692. Evaluate 1692 != 29, drop this branch.\n     |- Try 47 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 58 * 22 = 1276. Add 1276 to the number set. Current number set: [1276, 47], target: 29, just two numbers left.\n     |- Try 1276 + 47 = 1323. Evaluate 1323 != 29, drop this branch.\n     |- Try 1276 - 47 = 1229. Evaluate 1229 != 29, drop this branch.\n     |- Try 1276 * 47 = 59972. 59972 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1276 \/ 47 = 27.1. 27.1 is a decimal, drop this branch.\n    |- Try 58 \/ 22 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (47, 22) (numbers left: [58]). Try possible operations.\n    |- Try 47 + 22 = 69. Add 69 to the number set. Current number set: [69, 58], target: 29, just two numbers left.\n     |- Try 69 + 58 = 127. Evaluate 127 != 29, drop this branch.\n     |- Try 69 - 58 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 69 * 58 = 4002. 4002 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 58 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 - 22 = 25. Add 25 to the number set. Current number set: [25, 58], target: 29, just two numbers left.\n     |- Try 58 + 25 = 83. Evaluate 83 != 29, drop this branch.\n     |- Try 58 - 25 = 33. Evaluate 33 != 29, drop this branch.\n     |- Try 58 * 25 = 1450. Evaluate 1450 != 29, drop this branch.\n     |- Try 58 \/ 25 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 47 * 22 = 1034. Add 1034 to the number set. Current number set: [1034, 58], target: 29, just two numbers left.\n     |- Try 1034 + 58 = 1092. Evaluate 1092 != 29, drop this branch.\n     |- Try 1034 - 58 = 976. Evaluate 976 != 29, drop this branch.\n     |- Try 1034 * 58 = 59972. 59972 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1034 \/ 58 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 47 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 31 - 27 = 4. Add 4 to the number set. Current number set: [4, 47, 22], target: 29. Options for choosing two numbers: [(4, 47), (4, 22), (47, 22)].\n   |- Pick two numbers (4, 47) (numbers left: [22]). Try possible operations.\n    |- Try 47 + 4 = 51. Add 51 to the number set. Current number set: [51, 22], target: 29, just two numbers left.\n     |- Try 51 + 22 = 73. Evaluate 73 != 29, drop this branch.\n     |- Try 51 - 22 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 51 - 22 = 29\nThe step before: 47 + 4 = 51\nThe first step: 31 - 27 = 4\n\nOutput the solution in the required format:\n<Solution>\n31 - 27 = 4\n47 + 4 = 51\n51 - 22 = 29\n<\/Solution>\n","item":{"nums":[31,27,47,22],"solution":["31 - 27 = 4","47 + 4 = 51","51 - 22 = 29"],"target":29}}
+{"instance_id":"countdown_2k_160","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 15, 26, 12]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [4, 15, 26, 12], target: 49. Options for choosing two numbers: [(4, 15), (4, 26), (4, 12), (15, 26), (15, 12), (26, 12)].\n |- Pick two numbers (4, 15) (numbers left: [26, 12]). Try possible operations.\n  |- Try 15 + 4 = 19. Add 19 to the number set. Current number set: [19, 26, 12], target: 49. Options for choosing two numbers: [(19, 26), (19, 12), (26, 12)].\n   |- Pick two numbers (19, 26) (numbers left: [12]). Try possible operations.\n    |- Try 26 + 19 = 45. Add 45 to the number set. Current number set: [45, 12], target: 49, just two numbers left.\n     |- Try 45 + 12 = 57. Evaluate 57 != 49, drop this branch.\n     |- Try 45 - 12 = 33. Evaluate 33 != 49, drop this branch.\n     |- Try 45 * 12 = 540. Evaluate 540 != 49, drop this branch.\n     |- Try 45 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 26 - 19 = 7. Add 7 to the number set. Current number set: [7, 12], target: 49, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 49, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 49, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 49, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 26 * 19 = 494. Add 494 to the number set. Current number set: [494, 12], target: 49, just two numbers left.\n     |- Try 494 + 12 = 506. Evaluate 506 != 49, drop this branch.\n     |- Try 494 - 12 = 482. Evaluate 482 != 49, drop this branch.\n     |- Try 494 * 12 = 5928. 5928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 494 \/ 12 = 41.2. 41.2 is a decimal, drop this branch.\n    |- Try 26 \/ 19 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (19, 12) (numbers left: [26]). Try possible operations.\n    |- Try 19 + 12 = 31. Add 31 to the number set. Current number set: [31, 26], target: 49, just two numbers left.\n     |- Try 31 + 26 = 57. Evaluate 57 != 49, drop this branch.\n     |- Try 31 - 26 = 5. Evaluate 5 != 49, drop this branch.\n     |- Try 31 * 26 = 806. Evaluate 806 != 49, drop this branch.\n     |- Try 31 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 12 = 7. Add 7 to the number set. Current number set: [7, 26], target: 49, just two numbers left.\n     |- Try 26 + 7 = 33. Evaluate 33 != 49, drop this branch.\n     |- Try 26 - 7 = 19. Evaluate 19 != 49, drop this branch.\n     |- Try 26 * 7 = 182. Evaluate 182 != 49, drop this branch.\n     |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 19 * 12 = 228. Add 228 to the number set. Current number set: [228, 26], target: 49, just two numbers left.\n     |- Try 228 + 26 = 254. Evaluate 254 != 49, drop this branch.\n     |- Try 228 - 26 = 202. Evaluate 202 != 49, drop this branch.\n     |- Try 228 * 26 = 5928. 5928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 26 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (26, 12) (numbers left: [19]). Try possible operations.\n    |- Try 26 + 12 = 38. Add 38 to the number set. Current number set: [38, 19], target: 49, just two numbers left.\n     |- Try 38 + 19 = 57. Evaluate 57 != 49, drop this branch.\n     |- Try 38 - 19 = 19. Evaluate 19 != 49, drop this branch.\n     |- Try 38 * 19 = 722. Evaluate 722 != 49, drop this branch.\n     |- Try 38 \/ 19 = 2. Evaluate 2 != 49, drop this branch.\n    |- Try 26 - 12 = 14. Add 14 to the number set. Current number set: [14, 19], target: 49, just two numbers left.\n     |- Try 19 + 14 = 33. Evaluate 33 != 49, drop this branch.\n     |- Try 19 - 14 = 5. Evaluate 5 != 49, drop this branch.\n     |- Try 19 * 14 = 266. Evaluate 266 != 49, drop this branch.\n     |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 26 * 12 = 312. Add 312 to the number set. Current number set: [312, 19], target: 49, just two numbers left.\n     |- Try 312 + 19 = 331. Evaluate 331 != 49, drop this branch.\n     |- Try 312 - 19 = 293. Evaluate 293 != 49, drop this branch.\n     |- Try 312 * 19 = 5928. 5928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 19 = 16.4. 16.4 is a decimal, drop this branch.\n    |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 15 - 4 = 11. Add 11 to the number set. Current number set: [11, 26, 12], target: 49. Options for choosing two numbers: [(11, 26), (11, 12), (26, 12)].\n   |- Pick two numbers (11, 26) (numbers left: [12]). Try possible operations.\n    |- Try 26 + 11 = 37. Add 37 to the number set. Current number set: [37, 12], target: 49, just two numbers left.\n     |- Try 37 + 12 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 37 + 12 = 49\nThe step before: 26 + 11 = 37\nThe first step: 15 - 4 = 11\n\nOutput the solution in the required format:\n<Solution>\n15 - 4 = 11\n26 + 11 = 37\n37 + 12 = 49\n<\/Solution>\n","item":{"nums":[4,15,26,12],"solution":["15 - 4 = 11","26 + 11 = 37","37 + 12 = 49"],"target":49}}
+{"instance_id":"countdown_2k_161","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 6, 37, 37]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [18, 6, 37, 37], target: 25. Options for choosing two numbers: [(18, 6), (18, 37), (18, 37), (6, 37), (6, 37), (37, 37)].\n |- Pick two numbers (18, 6) (numbers left: [37, 37]). Try possible operations.\n  |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 37, 37], target: 25. Options for choosing two numbers: [(24, 37), (24, 37), (37, 37)].\n   |- Pick two numbers (24, 37) (numbers left: [37]). Try possible operations.\n    |- Try 37 + 24 = 61. Add 61 to the number set. Current number set: [61, 37], target: 25, just two numbers left.\n     |- Try 61 + 37 = 98. Evaluate 98 != 25, drop this branch.\n     |- Try 61 - 37 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 61 * 37 = 2257. 2257 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 - 24 = 13. Add 13 to the number set. Current number set: [13, 37], target: 25, just two numbers left.\n     |- Try 37 + 13 = 50. Evaluate 50 != 25, drop this branch.\n     |- Try 37 - 13 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 37 * 13 = 481. Evaluate 481 != 25, drop this branch.\n     |- Try 37 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 37 * 24 = 888. Add 888 to the number set. Current number set: [888, 37], target: 25, just two numbers left.\n     |- Try 888 + 37 = 925. Evaluate 925 != 25, drop this branch.\n     |- Try 888 - 37 = 851. Evaluate 851 != 25, drop this branch.\n     |- Try 888 * 37 = 32856. 32856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 888 \/ 37 = 24. Evaluate 24 != 25, drop this branch.\n    |- Try 37 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 37) (numbers left: [37]). Try possible operations.\n    |- Try 37 + 24 = 61. Add 61 to the number set. Current number set: [61, 37], target: 25, just two numbers left.\n     |- Try 61 + 37 = 98. Evaluate 98 != 25, drop this branch.\n     |- Try 61 - 37 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 61 * 37 = 2257. 2257 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 - 24 = 13. Add 13 to the number set. Current number set: [13, 37], target: 25, just two numbers left.\n     |- Try 37 + 13 = 50. Evaluate 50 != 25, drop this branch.\n     |- Try 37 - 13 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 37 * 13 = 481. Evaluate 481 != 25, drop this branch.\n     |- Try 37 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 37 * 24 = 888. Add 888 to the number set. Current number set: [888, 37], target: 25, just two numbers left.\n     |- Try 888 + 37 = 925. Evaluate 925 != 25, drop this branch.\n     |- Try 888 - 37 = 851. Evaluate 851 != 25, drop this branch.\n     |- Try 888 * 37 = 32856. 32856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 888 \/ 37 = 24. Evaluate 24 != 25, drop this branch.\n    |- Try 37 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (37, 37) (numbers left: [24]). Try possible operations.\n    |- Try 37 + 37 = 74. Add 74 to the number set. Current number set: [74, 24], target: 25, just two numbers left.\n     |- Try 74 + 24 = 98. Evaluate 98 != 25, drop this branch.\n     |- Try 74 - 24 = 50. Evaluate 50 != 25, drop this branch.\n     |- Try 74 * 24 = 1776. Evaluate 1776 != 25, drop this branch.\n     |- Try 74 \/ 24 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 37 - 37 = 0. Add 0 to the number set. Current number set: [0, 24], target: 25, just two numbers left.\n     |- Try 24 + 0 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 24 - 0 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 24 * 0 = 0. Evaluate 0 != 25, drop this branch.\n     |- Try 24 \/ 0 (invalid operation). drop this branch.\n    |- Try 37 * 37 = 1369. Add 1369 to the number set. Current number set: [1369, 24], target: 25, just two numbers left.\n     |- Try 1369 + 24 = 1393. Evaluate 1393 != 25, drop this branch.\n     |- Try 1369 - 24 = 1345. Evaluate 1345 != 25, drop this branch.\n     |- Try 1369 * 24 = 32856. 32856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1369 \/ 24 = 57.0. 57.0 is a decimal, drop this branch.\n    |- Try 37 \/ 37 = 1. Add 1 to the number set. Current number set: [1, 24], target: 25, just two numbers left.\n     |- Try 24 + 1 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 + 1 = 25\nThe step before: 37 \/ 37 = 1\nThe first step: 18 + 6 = 24\n\nOutput the solution in the required format:\n<Solution>\n18 + 6 = 24\n37 \/ 37 = 1\n24 + 1 = 25\n<\/Solution>\n","item":{"nums":[18,6,37,37],"solution":["18 + 6 = 24","37 \/ 37 = 1","24 + 1 = 25"],"target":25}}
+{"instance_id":"countdown_2k_162","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 31, 3, 4]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [37, 31, 3, 4], target: 12. Options for choosing two numbers: [(37, 31), (37, 3), (37, 4), (31, 3), (31, 4), (3, 4)].\n |- Pick two numbers (37, 31) (numbers left: [3, 4]). Try possible operations.\n  |- Try 37 + 31 = 68. Add 68 to the number set. Current number set: [68, 3, 4], target: 12. Options for choosing two numbers: [(68, 3), (68, 4), (3, 4)].\n   |- Pick two numbers (68, 3) (numbers left: [4]). Try possible operations.\n    |- Try 68 + 3 = 71. Add 71 to the number set. Current number set: [71, 4], target: 12, just two numbers left.\n     |- Try 71 + 4 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 71 - 4 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 71 * 4 = 284. Evaluate 284 != 12, drop this branch.\n     |- Try 71 \/ 4 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 68 - 3 = 65. Add 65 to the number set. Current number set: [65, 4], target: 12, just two numbers left.\n     |- Try 65 + 4 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 65 - 4 = 61. Evaluate 61 != 12, drop this branch.\n     |- Try 65 * 4 = 260. Evaluate 260 != 12, drop this branch.\n     |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 68 * 3 = 204. Add 204 to the number set. Current number set: [204, 4], target: 12, just two numbers left.\n     |- Try 204 + 4 = 208. Evaluate 208 != 12, drop this branch.\n     |- Try 204 - 4 = 200. Evaluate 200 != 12, drop this branch.\n     |- Try 204 * 4 = 816. Evaluate 816 != 12, drop this branch.\n     |- Try 204 \/ 4 = 51. Evaluate 51 != 12, drop this branch.\n    |- Try 68 \/ 3 = 22.7. 22.7 is a decimal, drop this branch.\n   |- Pick two numbers (68, 4) (numbers left: [3]). Try possible operations.\n    |- Try 68 + 4 = 72. Add 72 to the number set. Current number set: [72, 3], target: 12, just two numbers left.\n     |- Try 72 + 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 72 - 3 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 72 * 3 = 216. Evaluate 216 != 12, drop this branch.\n     |- Try 72 \/ 3 = 24. Evaluate 24 != 12, drop this branch.\n    |- Try 68 - 4 = 64. Add 64 to the number set. Current number set: [64, 3], target: 12, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 12, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 12, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 68 * 4 = 272. Add 272 to the number set. Current number set: [272, 3], target: 12, just two numbers left.\n     |- Try 272 + 3 = 275. Evaluate 275 != 12, drop this branch.\n     |- Try 272 - 3 = 269. Evaluate 269 != 12, drop this branch.\n     |- Try 272 * 3 = 816. Evaluate 816 != 12, drop this branch.\n     |- Try 272 \/ 3 = 90.7. 90.7 is a decimal, drop this branch.\n    |- Try 68 \/ 4 = 17. Add 17 to the number set. Current number set: [17, 3], target: 12, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 12, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 12, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (3, 4) (numbers left: [68]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 68], target: 12, just two numbers left.\n     |- Try 68 + 7 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 68 - 7 = 61. Evaluate 61 != 12, drop this branch.\n     |- Try 68 * 7 = 476. Evaluate 476 != 12, drop this branch.\n     |- Try 68 \/ 7 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 68], target: 12, just two numbers left.\n     |- Try 68 + 1 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 68 - 1 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 68 * 1 = 68. Evaluate 68 != 12, drop this branch.\n     |- Try 68 \/ 1 = 68. Evaluate 68 != 12, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 68], target: 12, just two numbers left.\n     |- Try 68 + 12 = 80. Evaluate 80 != 12, drop this branch.\n     |- Try 68 - 12 = 56. Evaluate 56 != 12, drop this branch.\n     |- Try 68 * 12 = 816. Evaluate 816 != 12, drop this branch.\n     |- Try 68 \/ 12 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 37 - 31 = 6. Add 6 to the number set. Current number set: [6, 3, 4], target: 12. Options for choosing two numbers: [(6, 3), (6, 4), (3, 4)].\n   |- Pick two numbers (6, 3) (numbers left: [4]). Try possible operations.\n    |- Try 6 + 3 = 9. Add 9 to the number set. Current number set: [9, 4], target: 12, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 6 - 3 = 3. Add 3 to the number set. Current number set: [3, 4], target: 12, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 4 * 3 = 12\nThe step before: 6 - 3 = 3\nThe first step: 37 - 31 = 6\n\nOutput the solution in the required format:\n<Solution>\n37 - 31 = 6\n6 - 3 = 3\n4 * 3 = 12\n<\/Solution>\n","item":{"nums":[37,31,3,4],"solution":["37 - 31 = 6","6 - 3 = 3","4 * 3 = 12"],"target":12}}
+{"instance_id":"countdown_2k_163","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 30, 3, 35]\nTarget: 39","reference_output":"# Search Procedure\nInitial number set: [18, 30, 3, 35], target: 39. Options for choosing two numbers: [(18, 30), (18, 3), (18, 35), (30, 3), (30, 35), (3, 35)].\n |- Pick two numbers (18, 30) (numbers left: [3, 35]). Try possible operations.\n  |- Try 30 + 18 = 48. Add 48 to the number set. Current number set: [48, 3, 35], target: 39. Options for choosing two numbers: [(48, 3), (48, 35), (3, 35)].\n   |- Pick two numbers (48, 3) (numbers left: [35]). Try possible operations.\n    |- Try 48 + 3 = 51. Add 51 to the number set. Current number set: [51, 35], target: 39, just two numbers left.\n     |- Try 51 + 35 = 86. Evaluate 86 != 39, drop this branch.\n     |- Try 51 - 35 = 16. Evaluate 16 != 39, drop this branch.\n     |- Try 51 * 35 = 1785. Evaluate 1785 != 39, drop this branch.\n     |- Try 51 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 3 = 45. Add 45 to the number set. Current number set: [45, 35], target: 39, just two numbers left.\n     |- Try 45 + 35 = 80. Evaluate 80 != 39, drop this branch.\n     |- Try 45 - 35 = 10. Evaluate 10 != 39, drop this branch.\n     |- Try 45 * 35 = 1575. Evaluate 1575 != 39, drop this branch.\n     |- Try 45 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 * 3 = 144. Add 144 to the number set. Current number set: [144, 35], target: 39, just two numbers left.\n     |- Try 144 + 35 = 179. Evaluate 179 != 39, drop this branch.\n     |- Try 144 - 35 = 109. Evaluate 109 != 39, drop this branch.\n     |- Try 144 * 35 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 35 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 48 \/ 3 = 16. Add 16 to the number set. Current number set: [16, 35], target: 39, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 39, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 39, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 39, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (48, 35) (numbers left: [3]). Try possible operations.\n    |- Try 48 + 35 = 83. Add 83 to the number set. Current number set: [83, 3], target: 39, just two numbers left.\n     |- Try 83 + 3 = 86. Evaluate 86 != 39, drop this branch.\n     |- Try 83 - 3 = 80. Evaluate 80 != 39, drop this branch.\n     |- Try 83 * 3 = 249. Evaluate 249 != 39, drop this branch.\n     |- Try 83 \/ 3 = 27.7. 27.7 is a decimal, drop this branch.\n    |- Try 48 - 35 = 13. Add 13 to the number set. Current number set: [13, 3], target: 39, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 39, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 39, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 == 39, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 13 * 3 = 39\nThe step before: 48 - 35 = 13\nThe first step: 30 + 18 = 48\n\nOutput the solution in the required format:\n<Solution>\n30 + 18 = 48\n48 - 35 = 13\n13 * 3 = 39\n<\/Solution>\n","item":{"nums":[18,30,3,35],"solution":["30 + 18 = 48","48 - 35 = 13","13 * 3 = 39"],"target":39}}
+{"instance_id":"countdown_2k_164","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [11, 45, 28, 23]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [11, 45, 28, 23], target: 29. Options for choosing two numbers: [(11, 45), (11, 28), (11, 23), (45, 28), (45, 23), (28, 23)].\n |- Pick two numbers (11, 45) (numbers left: [28, 23]). Try possible operations.\n  |- Try 45 + 11 = 56. Add 56 to the number set. Current number set: [56, 28, 23], target: 29. Options for choosing two numbers: [(56, 28), (56, 23), (28, 23)].\n   |- Pick two numbers (56, 28) (numbers left: [23]). Try possible operations.\n    |- Try 56 + 28 = 84. Add 84 to the number set. Current number set: [84, 23], target: 29, just two numbers left.\n     |- Try 84 + 23 = 107. Evaluate 107 != 29, drop this branch.\n     |- Try 84 - 23 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 84 * 23 = 1932. Evaluate 1932 != 29, drop this branch.\n     |- Try 84 \/ 23 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 56 - 28 = 28. Add 28 to the number set. Current number set: [28, 23], target: 29, just two numbers left.\n     |- Try 28 + 23 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 28 - 23 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 28 * 23 = 644. Evaluate 644 != 29, drop this branch.\n     |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 56 * 28 = 1568. Add 1568 to the number set. Current number set: [1568, 23], target: 29, just two numbers left.\n     |- Try 1568 + 23 = 1591. Evaluate 1591 != 29, drop this branch.\n     |- Try 1568 - 23 = 1545. Evaluate 1545 != 29, drop this branch.\n     |- Try 1568 * 23 = 36064. 36064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1568 \/ 23 = 68.2. 68.2 is a decimal, drop this branch.\n    |- Try 56 \/ 28 = 2. Add 2 to the number set. Current number set: [2, 23], target: 29, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 != 29, drop this branch.\n     |- Try 23 - 2 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 23 * 2 = 46. Evaluate 46 != 29, drop this branch.\n     |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (56, 23) (numbers left: [28]). Try possible operations.\n    |- Try 56 + 23 = 79. Add 79 to the number set. Current number set: [79, 28], target: 29, just two numbers left.\n     |- Try 79 + 28 = 107. Evaluate 107 != 29, drop this branch.\n     |- Try 79 - 28 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 79 * 28 = 2212. 2212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 28 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 56 - 23 = 33. Add 33 to the number set. Current number set: [33, 28], target: 29, just two numbers left.\n     |- Try 33 + 28 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 33 - 28 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 33 * 28 = 924. Evaluate 924 != 29, drop this branch.\n     |- Try 33 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 56 * 23 = 1288. Add 1288 to the number set. Current number set: [1288, 28], target: 29, just two numbers left.\n     |- Try 1288 + 28 = 1316. Evaluate 1316 != 29, drop this branch.\n     |- Try 1288 - 28 = 1260. Evaluate 1260 != 29, drop this branch.\n     |- Try 1288 * 28 = 36064. 36064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1288 \/ 28 = 46. Evaluate 46 != 29, drop this branch.\n    |- Try 56 \/ 23 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 23) (numbers left: [56]). Try possible operations.\n    |- Try 28 + 23 = 51. Add 51 to the number set. Current number set: [51, 56], target: 29, just two numbers left.\n     |- Try 56 + 51 = 107. Evaluate 107 != 29, drop this branch.\n     |- Try 56 - 51 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 56 * 51 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 51 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 23 = 5. Add 5 to the number set. Current number set: [5, 56], target: 29, just two numbers left.\n     |- Try 56 + 5 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 56 - 5 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 56 * 5 = 280. Evaluate 280 != 29, drop this branch.\n     |- Try 56 \/ 5 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 28 * 23 = 644. Add 644 to the number set. Current number set: [644, 56], target: 29, just two numbers left.\n     |- Try 644 + 56 = 700. Evaluate 700 != 29, drop this branch.\n     |- Try 644 - 56 = 588. Evaluate 588 != 29, drop this branch.\n     |- Try 644 * 56 = 36064. 36064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 644 \/ 56 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 45 - 11 = 34. Add 34 to the number set. Current number set: [34, 28, 23], target: 29. Options for choosing two numbers: [(34, 28), (34, 23), (28, 23)].\n   |- Pick two numbers (34, 28) (numbers left: [23]). Try possible operations.\n    |- Try 34 + 28 = 62. Add 62 to the number set. Current number set: [62, 23], target: 29, just two numbers left.\n     |- Try 62 + 23 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 62 - 23 = 39. Evaluate 39 != 29, drop this branch.\n     |- Try 62 * 23 = 1426. Evaluate 1426 != 29, drop this branch.\n     |- Try 62 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 34 - 28 = 6. Add 6 to the number set. Current number set: [6, 23], target: 29, just two numbers left.\n     |- Try 23 + 6 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 6 = 29\nThe step before: 34 - 28 = 6\nThe first step: 45 - 11 = 34\n\nOutput the solution in the required format:\n<Solution>\n45 - 11 = 34\n34 - 28 = 6\n23 + 6 = 29\n<\/Solution>\n","item":{"nums":[11,45,28,23],"solution":["45 - 11 = 34","34 - 28 = 6","23 + 6 = 29"],"target":29}}
+{"instance_id":"countdown_2k_165","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 14, 15, 30]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [27, 14, 15, 30], target: 28. Options for choosing two numbers: [(27, 14), (27, 15), (27, 30), (14, 15), (14, 30), (15, 30)].\n |- Pick two numbers (27, 14) (numbers left: [15, 30]). Try possible operations.\n  |- Try 27 + 14 = 41. Add 41 to the number set. Current number set: [41, 15, 30], target: 28. Options for choosing two numbers: [(41, 15), (41, 30), (15, 30)].\n   |- Pick two numbers (41, 15) (numbers left: [30]). Try possible operations.\n    |- Try 41 + 15 = 56. Add 56 to the number set. Current number set: [56, 30], target: 28, just two numbers left.\n     |- Try 56 + 30 = 86. Evaluate 86 != 28, drop this branch.\n     |- Try 56 - 30 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 56 * 30 = 1680. Evaluate 1680 != 28, drop this branch.\n     |- Try 56 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 41 - 15 = 26. Add 26 to the number set. Current number set: [26, 30], target: 28, just two numbers left.\n     |- Try 30 + 26 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 30 - 26 = 4. Evaluate 4 != 28, drop this branch.\n     |- Try 30 * 26 = 780. Evaluate 780 != 28, drop this branch.\n     |- Try 30 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 15 = 615. Add 615 to the number set. Current number set: [615, 30], target: 28, just two numbers left.\n     |- Try 615 + 30 = 645. Evaluate 645 != 28, drop this branch.\n     |- Try 615 - 30 = 585. Evaluate 585 != 28, drop this branch.\n     |- Try 615 * 30 = 18450. 18450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 615 \/ 30 = 20.5. 20.5 is a decimal, drop this branch.\n    |- Try 41 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (41, 30) (numbers left: [15]). Try possible operations.\n    |- Try 41 + 30 = 71. Add 71 to the number set. Current number set: [71, 15], target: 28, just two numbers left.\n     |- Try 71 + 15 = 86. Evaluate 86 != 28, drop this branch.\n     |- Try 71 - 15 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 71 * 15 = 1065. Evaluate 1065 != 28, drop this branch.\n     |- Try 71 \/ 15 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 41 - 30 = 11. Add 11 to the number set. Current number set: [11, 15], target: 28, just two numbers left.\n     |- Try 15 + 11 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 15 - 11 = 4. Evaluate 4 != 28, drop this branch.\n     |- Try 15 * 11 = 165. Evaluate 165 != 28, drop this branch.\n     |- Try 15 \/ 11 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 41 * 30 = 1230. Add 1230 to the number set. Current number set: [1230, 15], target: 28, just two numbers left.\n     |- Try 1230 + 15 = 1245. Evaluate 1245 != 28, drop this branch.\n     |- Try 1230 - 15 = 1215. Evaluate 1215 != 28, drop this branch.\n     |- Try 1230 * 15 = 18450. 18450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 15 = 82. Evaluate 82 != 28, drop this branch.\n    |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (15, 30) (numbers left: [41]). Try possible operations.\n    |- Try 30 + 15 = 45. Add 45 to the number set. Current number set: [45, 41], target: 28, just two numbers left.\n     |- Try 45 + 41 = 86. Evaluate 86 != 28, drop this branch.\n     |- Try 45 - 41 = 4. Evaluate 4 != 28, drop this branch.\n     |- Try 45 * 41 = 1845. Evaluate 1845 != 28, drop this branch.\n     |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 - 15 = 15. Add 15 to the number set. Current number set: [15, 41], target: 28, just two numbers left.\n     |- Try 41 + 15 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 41 - 15 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 41 * 15 = 615. Evaluate 615 != 28, drop this branch.\n     |- Try 41 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 30 * 15 = 450. Add 450 to the number set. Current number set: [450, 41], target: 28, just two numbers left.\n     |- Try 450 + 41 = 491. Evaluate 491 != 28, drop this branch.\n     |- Try 450 - 41 = 409. Evaluate 409 != 28, drop this branch.\n     |- Try 450 * 41 = 18450. 18450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 41 = 11.0. 11.0 is a decimal, drop this branch.\n    |- Try 30 \/ 15 = 2. Add 2 to the number set. Current number set: [2, 41], target: 28, just two numbers left.\n     |- Try 41 + 2 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 41 - 2 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 41 * 2 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 41 \/ 2 = 20.5. 20.5 is a decimal, drop this branch.\n  |- Try 27 - 14 = 13. Add 13 to the number set. Current number set: [13, 15, 30], target: 28. Options for choosing two numbers: [(13, 15), (13, 30), (15, 30)].\n   |- Pick two numbers (13, 15) (numbers left: [30]). Try possible operations.\n    |- Try 15 + 13 = 28. Add 28 to the number set. Current number set: [28, 30], target: 28, just two numbers left.\n     |- Try 30 + 28 = 58. Evaluate 58 != 28, drop this branch.\n     |- Try 30 - 28 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 30 * 28 = 840. Evaluate 840 != 28, drop this branch.\n     |- Try 30 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 15 - 13 = 2. Add 2 to the number set. Current number set: [2, 30], target: 28, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 - 2 = 28\nThe step before: 15 - 13 = 2\nThe first step: 27 - 14 = 13\n\nOutput the solution in the required format:\n<Solution>\n27 - 14 = 13\n15 - 13 = 2\n30 - 2 = 28\n<\/Solution>\n","item":{"nums":[27,14,15,30],"solution":["27 - 14 = 13","15 - 13 = 2","30 - 2 = 28"],"target":28}}
+{"instance_id":"countdown_2k_166","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 27, 44, 16]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [20, 27, 44, 16], target: 35. Options for choosing two numbers: [(20, 27), (20, 44), (20, 16), (27, 44), (27, 16), (44, 16)].\n |- Pick two numbers (20, 27) (numbers left: [44, 16]). Try possible operations.\n  |- Try 27 + 20 = 47. Add 47 to the number set. Current number set: [47, 44, 16], target: 35. Options for choosing two numbers: [(47, 44), (47, 16), (44, 16)].\n   |- Pick two numbers (47, 44) (numbers left: [16]). Try possible operations.\n    |- Try 47 + 44 = 91. Add 91 to the number set. Current number set: [91, 16], target: 35, just two numbers left.\n     |- Try 91 + 16 = 107. Evaluate 107 != 35, drop this branch.\n     |- Try 91 - 16 = 75. Evaluate 75 != 35, drop this branch.\n     |- Try 91 * 16 = 1456. Evaluate 1456 != 35, drop this branch.\n     |- Try 91 \/ 16 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 47 - 44 = 3. Add 3 to the number set. Current number set: [3, 16], target: 35, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 35, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 35, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 47 * 44 = 2068. 2068 exceeds the maximum intermediate result, drop this branch.\n    |- Try 47 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (47, 16) (numbers left: [44]). Try possible operations.\n    |- Try 47 + 16 = 63. Add 63 to the number set. Current number set: [63, 44], target: 35, just two numbers left.\n     |- Try 63 + 44 = 107. Evaluate 107 != 35, drop this branch.\n     |- Try 63 - 44 = 19. Evaluate 19 != 35, drop this branch.\n     |- Try 63 * 44 = 2772. 2772 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 47 - 16 = 31. Add 31 to the number set. Current number set: [31, 44], target: 35, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 35, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 != 35, drop this branch.\n     |- Try 44 * 31 = 1364. Evaluate 1364 != 35, drop this branch.\n     |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 47 * 16 = 752. Add 752 to the number set. Current number set: [752, 44], target: 35, just two numbers left.\n     |- Try 752 + 44 = 796. Evaluate 796 != 35, drop this branch.\n     |- Try 752 - 44 = 708. Evaluate 708 != 35, drop this branch.\n     |- Try 752 * 44 = 33088. 33088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 752 \/ 44 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 47 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 16) (numbers left: [47]). Try possible operations.\n    |- Try 44 + 16 = 60. Add 60 to the number set. Current number set: [60, 47], target: 35, just two numbers left.\n     |- Try 60 + 47 = 107. Evaluate 107 != 35, drop this branch.\n     |- Try 60 - 47 = 13. Evaluate 13 != 35, drop this branch.\n     |- Try 60 * 47 = 2820. 2820 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 47 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 44 - 16 = 28. Add 28 to the number set. Current number set: [28, 47], target: 35, just two numbers left.\n     |- Try 47 + 28 = 75. Evaluate 75 != 35, drop this branch.\n     |- Try 47 - 28 = 19. Evaluate 19 != 35, drop this branch.\n     |- Try 47 * 28 = 1316. Evaluate 1316 != 35, drop this branch.\n     |- Try 47 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 44 * 16 = 704. Add 704 to the number set. Current number set: [704, 47], target: 35, just two numbers left.\n     |- Try 704 + 47 = 751. Evaluate 751 != 35, drop this branch.\n     |- Try 704 - 47 = 657. Evaluate 657 != 35, drop this branch.\n     |- Try 704 * 47 = 33088. 33088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 704 \/ 47 = 15.0. 15.0 is a decimal, drop this branch.\n    |- Try 44 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 27 - 20 = 7. Add 7 to the number set. Current number set: [7, 44, 16], target: 35. Options for choosing two numbers: [(7, 44), (7, 16), (44, 16)].\n   |- Pick two numbers (7, 44) (numbers left: [16]). Try possible operations.\n    |- Try 44 + 7 = 51. Add 51 to the number set. Current number set: [51, 16], target: 35, just two numbers left.\n     |- Try 51 + 16 = 67. Evaluate 67 != 35, drop this branch.\n     |- Try 51 - 16 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 51 - 16 = 35\nThe step before: 44 + 7 = 51\nThe first step: 27 - 20 = 7\n\nOutput the solution in the required format:\n<Solution>\n27 - 20 = 7\n44 + 7 = 51\n51 - 16 = 35\n<\/Solution>\n","item":{"nums":[20,27,44,16],"solution":["27 - 20 = 7","44 + 7 = 51","51 - 16 = 35"],"target":35}}
+{"instance_id":"countdown_2k_167","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 3, 1, 2]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [27, 3, 1, 2], target: 10. Options for choosing two numbers: [(27, 3), (27, 1), (27, 2), (3, 1), (3, 2), (1, 2)].\n |- Pick two numbers (27, 3) (numbers left: [1, 2]). Try possible operations.\n  |- Try 27 + 3 = 30. Add 30 to the number set. Current number set: [30, 1, 2], target: 10. Options for choosing two numbers: [(30, 1), (30, 2), (1, 2)].\n   |- Pick two numbers (30, 1) (numbers left: [2]). Try possible operations.\n    |- Try 30 + 1 = 31. Add 31 to the number set. Current number set: [31, 2], target: 10, just two numbers left.\n     |- Try 31 + 2 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 31 - 2 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 31 * 2 = 62. Evaluate 62 != 10, drop this branch.\n     |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 30 - 1 = 29. Add 29 to the number set. Current number set: [29, 2], target: 10, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 != 10, drop this branch.\n     |- Try 29 - 2 = 27. Evaluate 27 != 10, drop this branch.\n     |- Try 29 * 2 = 58. Evaluate 58 != 10, drop this branch.\n     |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 30 * 1 = 30. Add 30 to the number set. Current number set: [30, 2], target: 10, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 10, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 10, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 != 10, drop this branch.\n    |- Try 30 \/ 1 = 30. Add 30 to the number set. Current number set: [30, 2], target: 10, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 10, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 10, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 != 10, drop this branch.\n   |- Pick two numbers (30, 2) (numbers left: [1]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 1], target: 10, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 10, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 10, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 10, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 1], target: 10, just two numbers left.\n     |- Try 28 + 1 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 28 - 1 = 27. Evaluate 27 != 10, drop this branch.\n     |- Try 28 * 1 = 28. Evaluate 28 != 10, drop this branch.\n     |- Try 28 \/ 1 = 28. Evaluate 28 != 10, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 1], target: 10, just two numbers left.\n     |- Try 60 + 1 = 61. Evaluate 61 != 10, drop this branch.\n     |- Try 60 - 1 = 59. Evaluate 59 != 10, drop this branch.\n     |- Try 60 * 1 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 60 \/ 1 = 60. Evaluate 60 != 10, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 1], target: 10, just two numbers left.\n     |- Try 15 + 1 = 16. Evaluate 16 != 10, drop this branch.\n     |- Try 15 - 1 = 14. Evaluate 14 != 10, drop this branch.\n     |- Try 15 * 1 = 15. Evaluate 15 != 10, drop this branch.\n     |- Try 15 \/ 1 = 15. Evaluate 15 != 10, drop this branch.\n   |- Pick two numbers (1, 2) (numbers left: [30]). Try possible operations.\n    |- Try 2 + 1 = 3. Add 3 to the number set. Current number set: [3, 30], target: 10, just two numbers left.\n     |- Try 30 + 3 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 30 - 3 = 27. Evaluate 27 != 10, drop this branch.\n     |- Try 30 * 3 = 90. Evaluate 90 != 10, drop this branch.\n     |- Try 30 \/ 3 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 \/ 3 = 10\nThe step before: 2 + 1 = 3\nThe first step: 27 + 3 = 30\n\nOutput the solution in the required format:\n<Solution>\n27 + 3 = 30\n2 + 1 = 3\n30 \/ 3 = 10\n<\/Solution>\n","item":{"nums":[27,3,1,2],"solution":["27 + 3 = 30","2 + 1 = 3","30 \/ 3 = 10"],"target":10}}
+{"instance_id":"countdown_2k_168","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 34, 48, 39]\nTarget: 19","reference_output":"# Search Procedure\nInitial number set: [24, 34, 48, 39], target: 19. Options for choosing two numbers: [(24, 34), (24, 48), (24, 39), (34, 48), (34, 39), (48, 39)].\n |- Pick two numbers (24, 34) (numbers left: [48, 39]). Try possible operations.\n  |- Try 34 + 24 = 58. Add 58 to the number set. Current number set: [58, 48, 39], target: 19. Options for choosing two numbers: [(58, 48), (58, 39), (48, 39)].\n   |- Pick two numbers (58, 48) (numbers left: [39]). Try possible operations.\n    |- Try 58 + 48 = 106. Add 106 to the number set. Current number set: [106, 39], target: 19, just two numbers left.\n     |- Try 106 + 39 = 145. Evaluate 145 != 19, drop this branch.\n     |- Try 106 - 39 = 67. Evaluate 67 != 19, drop this branch.\n     |- Try 106 * 39 = 4134. 4134 exceeds the maximum intermediate result, drop this branch.\n     |- Try 106 \/ 39 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 58 - 48 = 10. Add 10 to the number set. Current number set: [10, 39], target: 19, just two numbers left.\n     |- Try 39 + 10 = 49. Evaluate 49 != 19, drop this branch.\n     |- Try 39 - 10 = 29. Evaluate 29 != 19, drop this branch.\n     |- Try 39 * 10 = 390. Evaluate 390 != 19, drop this branch.\n     |- Try 39 \/ 10 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 58 * 48 = 2784. 2784 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (58, 39) (numbers left: [48]). Try possible operations.\n    |- Try 58 + 39 = 97. Add 97 to the number set. Current number set: [97, 48], target: 19, just two numbers left.\n     |- Try 97 + 48 = 145. Evaluate 145 != 19, drop this branch.\n     |- Try 97 - 48 = 49. Evaluate 49 != 19, drop this branch.\n     |- Try 97 * 48 = 4656. 4656 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 48 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 58 - 39 = 19. Add 19 to the number set. Current number set: [19, 48], target: 19, just two numbers left.\n     |- Try 48 + 19 = 67. Evaluate 67 != 19, drop this branch.\n     |- Try 48 - 19 = 29. Evaluate 29 != 19, drop this branch.\n     |- Try 48 * 19 = 912. Evaluate 912 != 19, drop this branch.\n     |- Try 48 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 58 * 39 = 2262. 2262 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 39 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (48, 39) (numbers left: [58]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 58], target: 19, just two numbers left.\n     |- Try 87 + 58 = 145. Evaluate 145 != 19, drop this branch.\n     |- Try 87 - 58 = 29. Evaluate 29 != 19, drop this branch.\n     |- Try 87 * 58 = 5046. 5046 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 58 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 58], target: 19, just two numbers left.\n     |- Try 58 + 9 = 67. Evaluate 67 != 19, drop this branch.\n     |- Try 58 - 9 = 49. Evaluate 49 != 19, drop this branch.\n     |- Try 58 * 9 = 522. Evaluate 522 != 19, drop this branch.\n     |- Try 58 \/ 9 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 58], target: 19, just two numbers left.\n     |- Try 1872 + 58 = 1930. Evaluate 1930 != 19, drop this branch.\n     |- Try 1872 - 58 = 1814. Evaluate 1814 != 19, drop this branch.\n     |- Try 1872 * 58 = 108576. 108576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 58 = 32.3. 32.3 is a decimal, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 34 - 24 = 10. Add 10 to the number set. Current number set: [10, 48, 39], target: 19. Options for choosing two numbers: [(10, 48), (10, 39), (48, 39)].\n   |- Pick two numbers (10, 48) (numbers left: [39]). Try possible operations.\n    |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 39], target: 19, just two numbers left.\n     |- Try 58 + 39 = 97. Evaluate 97 != 19, drop this branch.\n     |- Try 58 - 39 = 19. Evaluate 19 == 19, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 58 - 39 = 19\nThe step before: 48 + 10 = 58\nThe first step: 34 - 24 = 10\n\nOutput the solution in the required format:\n<Solution>\n34 - 24 = 10\n48 + 10 = 58\n58 - 39 = 19\n<\/Solution>\n","item":{"nums":[24,34,48,39],"solution":["34 - 24 = 10","48 + 10 = 58","58 - 39 = 19"],"target":19}}
+{"instance_id":"countdown_2k_169","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [16, 36, 26, 13]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [16, 36, 26, 13], target: 30. Options for choosing two numbers: [(16, 36), (16, 26), (16, 13), (36, 26), (36, 13), (26, 13)].\n |- Pick two numbers (16, 36) (numbers left: [26, 13]). Try possible operations.\n  |- Try 36 + 16 = 52. Add 52 to the number set. Current number set: [52, 26, 13], target: 30. Options for choosing two numbers: [(52, 26), (52, 13), (26, 13)].\n   |- Pick two numbers (52, 26) (numbers left: [13]). Try possible operations.\n    |- Try 52 + 26 = 78. Add 78 to the number set. Current number set: [78, 13], target: 30, just two numbers left.\n     |- Try 78 + 13 = 91. Evaluate 91 != 30, drop this branch.\n     |- Try 78 - 13 = 65. Evaluate 65 != 30, drop this branch.\n     |- Try 78 * 13 = 1014. Evaluate 1014 != 30, drop this branch.\n     |- Try 78 \/ 13 = 6. Evaluate 6 != 30, drop this branch.\n    |- Try 52 - 26 = 26. Add 26 to the number set. Current number set: [26, 13], target: 30, just two numbers left.\n     |- Try 26 + 13 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 26 - 13 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 26 * 13 = 338. Evaluate 338 != 30, drop this branch.\n     |- Try 26 \/ 13 = 2. Evaluate 2 != 30, drop this branch.\n    |- Try 52 * 26 = 1352. Add 1352 to the number set. Current number set: [1352, 13], target: 30, just two numbers left.\n     |- Try 1352 + 13 = 1365. Evaluate 1365 != 30, drop this branch.\n     |- Try 1352 - 13 = 1339. Evaluate 1339 != 30, drop this branch.\n     |- Try 1352 * 13 = 17576. 17576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1352 \/ 13 = 104. Evaluate 104 != 30, drop this branch.\n    |- Try 52 \/ 26 = 2. Add 2 to the number set. Current number set: [2, 13], target: 30, just two numbers left.\n     |- Try 13 + 2 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 13 - 2 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 13 * 2 = 26. Evaluate 26 != 30, drop this branch.\n     |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (52, 13) (numbers left: [26]). Try possible operations.\n    |- Try 52 + 13 = 65. Add 65 to the number set. Current number set: [65, 26], target: 30, just two numbers left.\n     |- Try 65 + 26 = 91. Evaluate 91 != 30, drop this branch.\n     |- Try 65 - 26 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 65 * 26 = 1690. Evaluate 1690 != 30, drop this branch.\n     |- Try 65 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 52 - 13 = 39. Add 39 to the number set. Current number set: [39, 26], target: 30, just two numbers left.\n     |- Try 39 + 26 = 65. Evaluate 65 != 30, drop this branch.\n     |- Try 39 - 26 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 39 * 26 = 1014. Evaluate 1014 != 30, drop this branch.\n     |- Try 39 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 52 * 13 = 676. Add 676 to the number set. Current number set: [676, 26], target: 30, just two numbers left.\n     |- Try 676 + 26 = 702. Evaluate 702 != 30, drop this branch.\n     |- Try 676 - 26 = 650. Evaluate 650 != 30, drop this branch.\n     |- Try 676 * 26 = 17576. 17576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 676 \/ 26 = 26. Evaluate 26 != 30, drop this branch.\n    |- Try 52 \/ 13 = 4. Add 4 to the number set. Current number set: [4, 26], target: 30, just two numbers left.\n     |- Try 26 + 4 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 + 4 = 30\nThe step before: 52 \/ 13 = 4\nThe first step: 36 + 16 = 52\n\nOutput the solution in the required format:\n<Solution>\n36 + 16 = 52\n52 \/ 13 = 4\n26 + 4 = 30\n<\/Solution>\n","item":{"nums":[16,36,26,13],"solution":["36 + 16 = 52","52 \/ 13 = 4","26 + 4 = 30"],"target":30}}
+{"instance_id":"countdown_2k_170","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 26, 4, 37]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [42, 26, 4, 37], target: 49. Options for choosing two numbers: [(42, 26), (42, 4), (42, 37), (26, 4), (26, 37), (4, 37)].\n |- Pick two numbers (42, 26) (numbers left: [4, 37]). Try possible operations.\n  |- Try 42 + 26 = 68. Add 68 to the number set. Current number set: [68, 4, 37], target: 49. Options for choosing two numbers: [(68, 4), (68, 37), (4, 37)].\n   |- Pick two numbers (68, 4) (numbers left: [37]). Try possible operations.\n    |- Try 68 + 4 = 72. Add 72 to the number set. Current number set: [72, 37], target: 49, just two numbers left.\n     |- Try 72 + 37 = 109. Evaluate 109 != 49, drop this branch.\n     |- Try 72 - 37 = 35. Evaluate 35 != 49, drop this branch.\n     |- Try 72 * 37 = 2664. 2664 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 37 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 68 - 4 = 64. Add 64 to the number set. Current number set: [64, 37], target: 49, just two numbers left.\n     |- Try 64 + 37 = 101. Evaluate 101 != 49, drop this branch.\n     |- Try 64 - 37 = 27. Evaluate 27 != 49, drop this branch.\n     |- Try 64 * 37 = 2368. 2368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 37 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 68 * 4 = 272. Add 272 to the number set. Current number set: [272, 37], target: 49, just two numbers left.\n     |- Try 272 + 37 = 309. Evaluate 309 != 49, drop this branch.\n     |- Try 272 - 37 = 235. Evaluate 235 != 49, drop this branch.\n     |- Try 272 * 37 = 10064. 10064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 272 \/ 37 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 68 \/ 4 = 17. Add 17 to the number set. Current number set: [17, 37], target: 49, just two numbers left.\n     |- Try 37 + 17 = 54. Evaluate 54 != 49, drop this branch.\n     |- Try 37 - 17 = 20. Evaluate 20 != 49, drop this branch.\n     |- Try 37 * 17 = 629. Evaluate 629 != 49, drop this branch.\n     |- Try 37 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (68, 37) (numbers left: [4]). Try possible operations.\n    |- Try 68 + 37 = 105. Add 105 to the number set. Current number set: [105, 4], target: 49, just two numbers left.\n     |- Try 105 + 4 = 109. Evaluate 109 != 49, drop this branch.\n     |- Try 105 - 4 = 101. Evaluate 101 != 49, drop this branch.\n     |- Try 105 * 4 = 420. Evaluate 420 != 49, drop this branch.\n     |- Try 105 \/ 4 = 26.2. 26.2 is a decimal, drop this branch.\n    |- Try 68 - 37 = 31. Add 31 to the number set. Current number set: [31, 4], target: 49, just two numbers left.\n     |- Try 31 + 4 = 35. Evaluate 35 != 49, drop this branch.\n     |- Try 31 - 4 = 27. Evaluate 27 != 49, drop this branch.\n     |- Try 31 * 4 = 124. Evaluate 124 != 49, drop this branch.\n     |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 68 * 37 = 2516. 2516 exceeds the maximum intermediate result, drop this branch.\n    |- Try 68 \/ 37 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (4, 37) (numbers left: [68]). Try possible operations.\n    |- Try 37 + 4 = 41. Add 41 to the number set. Current number set: [41, 68], target: 49, just two numbers left.\n     |- Try 68 + 41 = 109. Evaluate 109 != 49, drop this branch.\n     |- Try 68 - 41 = 27. Evaluate 27 != 49, drop this branch.\n     |- Try 68 * 41 = 2788. 2788 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 41 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 37 - 4 = 33. Add 33 to the number set. Current number set: [33, 68], target: 49, just two numbers left.\n     |- Try 68 + 33 = 101. Evaluate 101 != 49, drop this branch.\n     |- Try 68 - 33 = 35. Evaluate 35 != 49, drop this branch.\n     |- Try 68 * 33 = 2244. 2244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 33 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 37 * 4 = 148. Add 148 to the number set. Current number set: [148, 68], target: 49, just two numbers left.\n     |- Try 148 + 68 = 216. Evaluate 216 != 49, drop this branch.\n     |- Try 148 - 68 = 80. Evaluate 80 != 49, drop this branch.\n     |- Try 148 * 68 = 10064. 10064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 148 \/ 68 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 37 \/ 4 = 9.2. 9.2 is a decimal, drop this branch.\n  |- Try 42 - 26 = 16. Add 16 to the number set. Current number set: [16, 4, 37], target: 49. Options for choosing two numbers: [(16, 4), (16, 37), (4, 37)].\n   |- Pick two numbers (16, 4) (numbers left: [37]). Try possible operations.\n    |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 37], target: 49, just two numbers left.\n     |- Try 37 + 20 = 57. Evaluate 57 != 49, drop this branch.\n     |- Try 37 - 20 = 17. Evaluate 17 != 49, drop this branch.\n     |- Try 37 * 20 = 740. Evaluate 740 != 49, drop this branch.\n     |- Try 37 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 37], target: 49, just two numbers left.\n     |- Try 37 + 12 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 37 + 12 = 49\nThe step before: 16 - 4 = 12\nThe first step: 42 - 26 = 16\n\nOutput the solution in the required format:\n<Solution>\n42 - 26 = 16\n16 - 4 = 12\n37 + 12 = 49\n<\/Solution>\n","item":{"nums":[42,26,4,37],"solution":["42 - 26 = 16","16 - 4 = 12","37 + 12 = 49"],"target":49}}
+{"instance_id":"countdown_2k_171","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 7, 32, 2]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [26, 7, 32, 2], target: 15. Options for choosing two numbers: [(26, 7), (26, 32), (26, 2), (7, 32), (7, 2), (32, 2)].\n |- Pick two numbers (26, 7) (numbers left: [32, 2]). Try possible operations.\n  |- Try 26 + 7 = 33. Add 33 to the number set. Current number set: [33, 32, 2], target: 15. Options for choosing two numbers: [(33, 32), (33, 2), (32, 2)].\n   |- Pick two numbers (33, 32) (numbers left: [2]). Try possible operations.\n    |- Try 33 + 32 = 65. Add 65 to the number set. Current number set: [65, 2], target: 15, just two numbers left.\n     |- Try 65 + 2 = 67. Evaluate 67 != 15, drop this branch.\n     |- Try 65 - 2 = 63. Evaluate 63 != 15, drop this branch.\n     |- Try 65 * 2 = 130. Evaluate 130 != 15, drop this branch.\n     |- Try 65 \/ 2 = 32.5. 32.5 is a decimal, drop this branch.\n    |- Try 33 - 32 = 1. Add 1 to the number set. Current number set: [1, 2], target: 15, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 15, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 15, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 15, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 15, drop this branch.\n    |- Try 33 * 32 = 1056. Add 1056 to the number set. Current number set: [1056, 2], target: 15, just two numbers left.\n     |- Try 1056 + 2 = 1058. Evaluate 1058 != 15, drop this branch.\n     |- Try 1056 - 2 = 1054. Evaluate 1054 != 15, drop this branch.\n     |- Try 1056 * 2 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 2 = 528. Evaluate 528 != 15, drop this branch.\n    |- Try 33 \/ 32 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (33, 2) (numbers left: [32]). Try possible operations.\n    |- Try 33 + 2 = 35. Add 35 to the number set. Current number set: [35, 32], target: 15, just two numbers left.\n     |- Try 35 + 32 = 67. Evaluate 67 != 15, drop this branch.\n     |- Try 35 - 32 = 3. Evaluate 3 != 15, drop this branch.\n     |- Try 35 * 32 = 1120. Evaluate 1120 != 15, drop this branch.\n     |- Try 35 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 - 2 = 31. Add 31 to the number set. Current number set: [31, 32], target: 15, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 15, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 15, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 15, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 * 2 = 66. Add 66 to the number set. Current number set: [66, 32], target: 15, just two numbers left.\n     |- Try 66 + 32 = 98. Evaluate 98 != 15, drop this branch.\n     |- Try 66 - 32 = 34. Evaluate 34 != 15, drop this branch.\n     |- Try 66 * 32 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 32 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [33]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 33], target: 15, just two numbers left.\n     |- Try 34 + 33 = 67. Evaluate 67 != 15, drop this branch.\n     |- Try 34 - 33 = 1. Evaluate 1 != 15, drop this branch.\n     |- Try 34 * 33 = 1122. Evaluate 1122 != 15, drop this branch.\n     |- Try 34 \/ 33 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 33], target: 15, just two numbers left.\n     |- Try 33 + 30 = 63. Evaluate 63 != 15, drop this branch.\n     |- Try 33 - 30 = 3. Evaluate 3 != 15, drop this branch.\n     |- Try 33 * 30 = 990. Evaluate 990 != 15, drop this branch.\n     |- Try 33 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 33], target: 15, just two numbers left.\n     |- Try 64 + 33 = 97. Evaluate 97 != 15, drop this branch.\n     |- Try 64 - 33 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 64 * 33 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 33 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 33], target: 15, just two numbers left.\n     |- Try 33 + 16 = 49. Evaluate 49 != 15, drop this branch.\n     |- Try 33 - 16 = 17. Evaluate 17 != 15, drop this branch.\n     |- Try 33 * 16 = 528. Evaluate 528 != 15, drop this branch.\n     |- Try 33 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 26 - 7 = 19. Add 19 to the number set. Current number set: [19, 32, 2], target: 15. Options for choosing two numbers: [(19, 32), (19, 2), (32, 2)].\n   |- Pick two numbers (19, 32) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 19 = 51. Add 51 to the number set. Current number set: [51, 2], target: 15, just two numbers left.\n     |- Try 51 + 2 = 53. Evaluate 53 != 15, drop this branch.\n     |- Try 51 - 2 = 49. Evaluate 49 != 15, drop this branch.\n     |- Try 51 * 2 = 102. Evaluate 102 != 15, drop this branch.\n     |- Try 51 \/ 2 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 32 - 19 = 13. Add 13 to the number set. Current number set: [13, 2], target: 15, just two numbers left.\n     |- Try 13 + 2 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 13 + 2 = 15\nThe step before: 32 - 19 = 13\nThe first step: 26 - 7 = 19\n\nOutput the solution in the required format:\n<Solution>\n26 - 7 = 19\n32 - 19 = 13\n13 + 2 = 15\n<\/Solution>\n","item":{"nums":[26,7,32,2],"solution":["26 - 7 = 19","32 - 19 = 13","13 + 2 = 15"],"target":15}}
+{"instance_id":"countdown_2k_172","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 24, 10, 21]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [24, 24, 10, 21], target: 21. Options for choosing two numbers: [(24, 24), (24, 10), (24, 21), (24, 10), (24, 21), (10, 21)].\n |- Pick two numbers (24, 24) (numbers left: [10, 21]). Try possible operations.\n  |- Try 24 + 24 = 48. Add 48 to the number set. Current number set: [48, 10, 21], target: 21. Options for choosing two numbers: [(48, 10), (48, 21), (10, 21)].\n   |- Pick two numbers (48, 10) (numbers left: [21]). Try possible operations.\n    |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 21], target: 21, just two numbers left.\n     |- Try 58 + 21 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 58 - 21 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 58 * 21 = 1218. Evaluate 1218 != 21, drop this branch.\n     |- Try 58 \/ 21 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 48 - 10 = 38. Add 38 to the number set. Current number set: [38, 21], target: 21, just two numbers left.\n     |- Try 38 + 21 = 59. Evaluate 59 != 21, drop this branch.\n     |- Try 38 - 21 = 17. Evaluate 17 != 21, drop this branch.\n     |- Try 38 * 21 = 798. Evaluate 798 != 21, drop this branch.\n     |- Try 38 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 * 10 = 480. Add 480 to the number set. Current number set: [480, 21], target: 21, just two numbers left.\n     |- Try 480 + 21 = 501. Evaluate 501 != 21, drop this branch.\n     |- Try 480 - 21 = 459. Evaluate 459 != 21, drop this branch.\n     |- Try 480 * 21 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 21 = 22.9. 22.9 is a decimal, drop this branch.\n    |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (48, 21) (numbers left: [10]). Try possible operations.\n    |- Try 48 + 21 = 69. Add 69 to the number set. Current number set: [69, 10], target: 21, just two numbers left.\n     |- Try 69 + 10 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 69 - 10 = 59. Evaluate 59 != 21, drop this branch.\n     |- Try 69 * 10 = 690. Evaluate 690 != 21, drop this branch.\n     |- Try 69 \/ 10 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 48 - 21 = 27. Add 27 to the number set. Current number set: [27, 10], target: 21, just two numbers left.\n     |- Try 27 + 10 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 27 - 10 = 17. Evaluate 17 != 21, drop this branch.\n     |- Try 27 * 10 = 270. Evaluate 270 != 21, drop this branch.\n     |- Try 27 \/ 10 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 48 * 21 = 1008. Add 1008 to the number set. Current number set: [1008, 10], target: 21, just two numbers left.\n     |- Try 1008 + 10 = 1018. Evaluate 1018 != 21, drop this branch.\n     |- Try 1008 - 10 = 998. Evaluate 998 != 21, drop this branch.\n     |- Try 1008 * 10 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 10 = 100.8. 100.8 is a decimal, drop this branch.\n    |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 21) (numbers left: [48]). Try possible operations.\n    |- Try 21 + 10 = 31. Add 31 to the number set. Current number set: [31, 48], target: 21, just two numbers left.\n     |- Try 48 + 31 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 48 - 31 = 17. Evaluate 17 != 21, drop this branch.\n     |- Try 48 * 31 = 1488. Evaluate 1488 != 21, drop this branch.\n     |- Try 48 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 21 - 10 = 11. Add 11 to the number set. Current number set: [11, 48], target: 21, just two numbers left.\n     |- Try 48 + 11 = 59. Evaluate 59 != 21, drop this branch.\n     |- Try 48 - 11 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 48 * 11 = 528. Evaluate 528 != 21, drop this branch.\n     |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 21 * 10 = 210. Add 210 to the number set. Current number set: [210, 48], target: 21, just two numbers left.\n     |- Try 210 + 48 = 258. Evaluate 258 != 21, drop this branch.\n     |- Try 210 - 48 = 162. Evaluate 162 != 21, drop this branch.\n     |- Try 210 * 48 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 48 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 24 - 24 = 0. Add 0 to the number set. Current number set: [0, 10, 21], target: 21. Options for choosing two numbers: [(0, 10), (0, 21), (10, 21)].\n   |- Pick two numbers (0, 10) (numbers left: [21]). Try possible operations.\n    |- Try 10 + 0 = 10. Add 10 to the number set. Current number set: [10, 21], target: 21, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 21, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 10 - 0 = 10. Add 10 to the number set. Current number set: [10, 21], target: 21, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 21, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 10 * 0 = 0. Add 0 to the number set. Current number set: [0, 21], target: 21, just two numbers left.\n     |- Try 21 + 0 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 + 0 = 21\nThe step before: 10 * 0 = 0\nThe first step: 24 - 24 = 0\n\nOutput the solution in the required format:\n<Solution>\n24 - 24 = 0\n10 * 0 = 0\n21 + 0 = 21\n<\/Solution>\n","item":{"nums":[24,24,10,21],"solution":["24 - 24 = 0","10 * 0 = 0","21 + 0 = 21"],"target":21}}
+{"instance_id":"countdown_2k_173","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 32, 42, 8]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [30, 32, 42, 8], target: 36. Options for choosing two numbers: [(30, 32), (30, 42), (30, 8), (32, 42), (32, 8), (42, 8)].\n |- Pick two numbers (30, 32) (numbers left: [42, 8]). Try possible operations.\n  |- Try 32 + 30 = 62. Add 62 to the number set. Current number set: [62, 42, 8], target: 36. Options for choosing two numbers: [(62, 42), (62, 8), (42, 8)].\n   |- Pick two numbers (62, 42) (numbers left: [8]). Try possible operations.\n    |- Try 62 + 42 = 104. Add 104 to the number set. Current number set: [104, 8], target: 36, just two numbers left.\n     |- Try 104 + 8 = 112. Evaluate 112 != 36, drop this branch.\n     |- Try 104 - 8 = 96. Evaluate 96 != 36, drop this branch.\n     |- Try 104 * 8 = 832. Evaluate 832 != 36, drop this branch.\n     |- Try 104 \/ 8 = 13. Evaluate 13 != 36, drop this branch.\n    |- Try 62 - 42 = 20. Add 20 to the number set. Current number set: [20, 8], target: 36, just two numbers left.\n     |- Try 20 + 8 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 20 - 8 = 12. Evaluate 12 != 36, drop this branch.\n     |- Try 20 * 8 = 160. Evaluate 160 != 36, drop this branch.\n     |- Try 20 \/ 8 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 62 * 42 = 2604. 2604 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (62, 8) (numbers left: [42]). Try possible operations.\n    |- Try 62 + 8 = 70. Add 70 to the number set. Current number set: [70, 42], target: 36, just two numbers left.\n     |- Try 70 + 42 = 112. Evaluate 112 != 36, drop this branch.\n     |- Try 70 - 42 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 70 * 42 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 42 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 62 - 8 = 54. Add 54 to the number set. Current number set: [54, 42], target: 36, just two numbers left.\n     |- Try 54 + 42 = 96. Evaluate 96 != 36, drop this branch.\n     |- Try 54 - 42 = 12. Evaluate 12 != 36, drop this branch.\n     |- Try 54 * 42 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 42 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 62 * 8 = 496. Add 496 to the number set. Current number set: [496, 42], target: 36, just two numbers left.\n     |- Try 496 + 42 = 538. Evaluate 538 != 36, drop this branch.\n     |- Try 496 - 42 = 454. Evaluate 454 != 36, drop this branch.\n     |- Try 496 * 42 = 20832. 20832 exceeds the maximum intermediate result, drop this branch.\n     |- Try 496 \/ 42 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 62 \/ 8 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (42, 8) (numbers left: [62]). Try possible operations.\n    |- Try 42 + 8 = 50. Add 50 to the number set. Current number set: [50, 62], target: 36, just two numbers left.\n     |- Try 62 + 50 = 112. Evaluate 112 != 36, drop this branch.\n     |- Try 62 - 50 = 12. Evaluate 12 != 36, drop this branch.\n     |- Try 62 * 50 = 3100. 3100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 50 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 - 8 = 34. Add 34 to the number set. Current number set: [34, 62], target: 36, just two numbers left.\n     |- Try 62 + 34 = 96. Evaluate 96 != 36, drop this branch.\n     |- Try 62 - 34 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 62 * 34 = 2108. 2108 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 34 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 42 * 8 = 336. Add 336 to the number set. Current number set: [336, 62], target: 36, just two numbers left.\n     |- Try 336 + 62 = 398. Evaluate 398 != 36, drop this branch.\n     |- Try 336 - 62 = 274. Evaluate 274 != 36, drop this branch.\n     |- Try 336 * 62 = 20832. 20832 exceeds the maximum intermediate result, drop this branch.\n     |- Try 336 \/ 62 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n  |- Try 32 - 30 = 2. Add 2 to the number set. Current number set: [2, 42, 8], target: 36. Options for choosing two numbers: [(2, 42), (2, 8), (42, 8)].\n   |- Pick two numbers (2, 42) (numbers left: [8]). Try possible operations.\n    |- Try 42 + 2 = 44. Add 44 to the number set. Current number set: [44, 8], target: 36, just two numbers left.\n     |- Try 44 + 8 = 52. Evaluate 52 != 36, drop this branch.\n     |- Try 44 - 8 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 8 = 36\nThe step before: 42 + 2 = 44\nThe first step: 32 - 30 = 2\n\nOutput the solution in the required format:\n<Solution>\n32 - 30 = 2\n42 + 2 = 44\n44 - 8 = 36\n<\/Solution>\n","item":{"nums":[30,32,42,8],"solution":["32 - 30 = 2","42 + 2 = 44","44 - 8 = 36"],"target":36}}
+{"instance_id":"countdown_2k_174","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 26, 33, 28]\nTarget: 45","reference_output":"# Search Procedure\nInitial number set: [10, 26, 33, 28], target: 45. Options for choosing two numbers: [(10, 26), (10, 33), (10, 28), (26, 33), (26, 28), (33, 28)].\n |- Pick two numbers (10, 26) (numbers left: [33, 28]). Try possible operations.\n  |- Try 26 + 10 = 36. Add 36 to the number set. Current number set: [36, 33, 28], target: 45. Options for choosing two numbers: [(36, 33), (36, 28), (33, 28)].\n   |- Pick two numbers (36, 33) (numbers left: [28]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 28], target: 45, just two numbers left.\n     |- Try 69 + 28 = 97. Evaluate 97 != 45, drop this branch.\n     |- Try 69 - 28 = 41. Evaluate 41 != 45, drop this branch.\n     |- Try 69 * 28 = 1932. Evaluate 1932 != 45, drop this branch.\n     |- Try 69 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 36 - 33 = 3. Add 3 to the number set. Current number set: [3, 28], target: 45, just two numbers left.\n     |- Try 28 + 3 = 31. Evaluate 31 != 45, drop this branch.\n     |- Try 28 - 3 = 25. Evaluate 25 != 45, drop this branch.\n     |- Try 28 * 3 = 84. Evaluate 84 != 45, drop this branch.\n     |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 36 * 33 = 1188. Add 1188 to the number set. Current number set: [1188, 28], target: 45, just two numbers left.\n     |- Try 1188 + 28 = 1216. Evaluate 1216 != 45, drop this branch.\n     |- Try 1188 - 28 = 1160. Evaluate 1160 != 45, drop this branch.\n     |- Try 1188 * 28 = 33264. 33264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 28 = 42.4. 42.4 is a decimal, drop this branch.\n    |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (36, 28) (numbers left: [33]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 33], target: 45, just two numbers left.\n     |- Try 64 + 33 = 97. Evaluate 97 != 45, drop this branch.\n     |- Try 64 - 33 = 31. Evaluate 31 != 45, drop this branch.\n     |- Try 64 * 33 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 33 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 33], target: 45, just two numbers left.\n     |- Try 33 + 8 = 41. Evaluate 41 != 45, drop this branch.\n     |- Try 33 - 8 = 25. Evaluate 25 != 45, drop this branch.\n     |- Try 33 * 8 = 264. Evaluate 264 != 45, drop this branch.\n     |- Try 33 \/ 8 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 33], target: 45, just two numbers left.\n     |- Try 1008 + 33 = 1041. Evaluate 1041 != 45, drop this branch.\n     |- Try 1008 - 33 = 975. Evaluate 975 != 45, drop this branch.\n     |- Try 1008 * 33 = 33264. 33264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 33 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (33, 28) (numbers left: [36]). Try possible operations.\n    |- Try 33 + 28 = 61. Add 61 to the number set. Current number set: [61, 36], target: 45, just two numbers left.\n     |- Try 61 + 36 = 97. Evaluate 97 != 45, drop this branch.\n     |- Try 61 - 36 = 25. Evaluate 25 != 45, drop this branch.\n     |- Try 61 * 36 = 2196. 2196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 36 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 33 - 28 = 5. Add 5 to the number set. Current number set: [5, 36], target: 45, just two numbers left.\n     |- Try 36 + 5 = 41. Evaluate 41 != 45, drop this branch.\n     |- Try 36 - 5 = 31. Evaluate 31 != 45, drop this branch.\n     |- Try 36 * 5 = 180. Evaluate 180 != 45, drop this branch.\n     |- Try 36 \/ 5 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 33 * 28 = 924. Add 924 to the number set. Current number set: [924, 36], target: 45, just two numbers left.\n     |- Try 924 + 36 = 960. Evaluate 960 != 45, drop this branch.\n     |- Try 924 - 36 = 888. Evaluate 888 != 45, drop this branch.\n     |- Try 924 * 36 = 33264. 33264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 36 = 25.7. 25.7 is a decimal, drop this branch.\n    |- Try 33 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 26 - 10 = 16. Add 16 to the number set. Current number set: [16, 33, 28], target: 45. Options for choosing two numbers: [(16, 33), (16, 28), (33, 28)].\n   |- Pick two numbers (16, 33) (numbers left: [28]). Try possible operations.\n    |- Try 33 + 16 = 49. Add 49 to the number set. Current number set: [49, 28], target: 45, just two numbers left.\n     |- Try 49 + 28 = 77. Evaluate 77 != 45, drop this branch.\n     |- Try 49 - 28 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 49 * 28 = 1372. Evaluate 1372 != 45, drop this branch.\n     |- Try 49 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 33 - 16 = 17. Add 17 to the number set. Current number set: [17, 28], target: 45, just two numbers left.\n     |- Try 28 + 17 = 45. Evaluate 45 == 45, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 + 17 = 45\nThe step before: 33 - 16 = 17\nThe first step: 26 - 10 = 16\n\nOutput the solution in the required format:\n<Solution>\n26 - 10 = 16\n33 - 16 = 17\n28 + 17 = 45\n<\/Solution>\n","item":{"nums":[10,26,33,28],"solution":["26 - 10 = 16","33 - 16 = 17","28 + 17 = 45"],"target":45}}
+{"instance_id":"countdown_2k_175","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [28, 7, 44, 4]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [28, 7, 44, 4], target: 27. Options for choosing two numbers: [(28, 7), (28, 44), (28, 4), (7, 44), (7, 4), (44, 4)].\n |- Pick two numbers (28, 7) (numbers left: [44, 4]). Try possible operations.\n  |- Try 28 + 7 = 35. Add 35 to the number set. Current number set: [35, 44, 4], target: 27. Options for choosing two numbers: [(35, 44), (35, 4), (44, 4)].\n   |- Pick two numbers (35, 44) (numbers left: [4]). Try possible operations.\n    |- Try 44 + 35 = 79. Add 79 to the number set. Current number set: [79, 4], target: 27, just two numbers left.\n     |- Try 79 + 4 = 83. Evaluate 83 != 27, drop this branch.\n     |- Try 79 - 4 = 75. Evaluate 75 != 27, drop this branch.\n     |- Try 79 * 4 = 316. Evaluate 316 != 27, drop this branch.\n     |- Try 79 \/ 4 = 19.8. 19.8 is a decimal, drop this branch.\n    |- Try 44 - 35 = 9. Add 9 to the number set. Current number set: [9, 4], target: 27, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 27, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 27, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 27, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 44 * 35 = 1540. Add 1540 to the number set. Current number set: [1540, 4], target: 27, just two numbers left.\n     |- Try 1540 + 4 = 1544. Evaluate 1544 != 27, drop this branch.\n     |- Try 1540 - 4 = 1536. Evaluate 1536 != 27, drop this branch.\n     |- Try 1540 * 4 = 6160. 6160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1540 \/ 4 = 385. Evaluate 385 != 27, drop this branch.\n    |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (35, 4) (numbers left: [44]). Try possible operations.\n    |- Try 35 + 4 = 39. Add 39 to the number set. Current number set: [39, 44], target: 27, just two numbers left.\n     |- Try 44 + 39 = 83. Evaluate 83 != 27, drop this branch.\n     |- Try 44 - 39 = 5. Evaluate 5 != 27, drop this branch.\n     |- Try 44 * 39 = 1716. Evaluate 1716 != 27, drop this branch.\n     |- Try 44 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 - 4 = 31. Add 31 to the number set. Current number set: [31, 44], target: 27, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 27, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 != 27, drop this branch.\n     |- Try 44 * 31 = 1364. Evaluate 1364 != 27, drop this branch.\n     |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 * 4 = 140. Add 140 to the number set. Current number set: [140, 44], target: 27, just two numbers left.\n     |- Try 140 + 44 = 184. Evaluate 184 != 27, drop this branch.\n     |- Try 140 - 44 = 96. Evaluate 96 != 27, drop this branch.\n     |- Try 140 * 44 = 6160. 6160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 44 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n   |- Pick two numbers (44, 4) (numbers left: [35]). Try possible operations.\n    |- Try 44 + 4 = 48. Add 48 to the number set. Current number set: [48, 35], target: 27, just two numbers left.\n     |- Try 48 + 35 = 83. Evaluate 83 != 27, drop this branch.\n     |- Try 48 - 35 = 13. Evaluate 13 != 27, drop this branch.\n     |- Try 48 * 35 = 1680. Evaluate 1680 != 27, drop this branch.\n     |- Try 48 \/ 35 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 4 = 40. Add 40 to the number set. Current number set: [40, 35], target: 27, just two numbers left.\n     |- Try 40 + 35 = 75. Evaluate 75 != 27, drop this branch.\n     |- Try 40 - 35 = 5. Evaluate 5 != 27, drop this branch.\n     |- Try 40 * 35 = 1400. Evaluate 1400 != 27, drop this branch.\n     |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 4 = 176. Add 176 to the number set. Current number set: [176, 35], target: 27, just two numbers left.\n     |- Try 176 + 35 = 211. Evaluate 211 != 27, drop this branch.\n     |- Try 176 - 35 = 141. Evaluate 141 != 27, drop this branch.\n     |- Try 176 * 35 = 6160. 6160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 35 = 5.0. 5.0 is a decimal, drop this branch.\n    |- Try 44 \/ 4 = 11. Add 11 to the number set. Current number set: [11, 35], target: 27, just two numbers left.\n     |- Try 35 + 11 = 46. Evaluate 46 != 27, drop this branch.\n     |- Try 35 - 11 = 24. Evaluate 24 != 27, drop this branch.\n     |- Try 35 * 11 = 385. Evaluate 385 != 27, drop this branch.\n     |- Try 35 \/ 11 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 28 - 7 = 21. Add 21 to the number set. Current number set: [21, 44, 4], target: 27. Options for choosing two numbers: [(21, 44), (21, 4), (44, 4)].\n   |- Pick two numbers (21, 44) (numbers left: [4]). Try possible operations.\n    |- Try 44 + 21 = 65. Add 65 to the number set. Current number set: [65, 4], target: 27, just two numbers left.\n     |- Try 65 + 4 = 69. Evaluate 69 != 27, drop this branch.\n     |- Try 65 - 4 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 65 * 4 = 260. Evaluate 260 != 27, drop this branch.\n     |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 44 - 21 = 23. Add 23 to the number set. Current number set: [23, 4], target: 27, just two numbers left.\n     |- Try 23 + 4 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 4 = 27\nThe step before: 44 - 21 = 23\nThe first step: 28 - 7 = 21\n\nOutput the solution in the required format:\n<Solution>\n28 - 7 = 21\n44 - 21 = 23\n23 + 4 = 27\n<\/Solution>\n","item":{"nums":[28,7,44,4],"solution":["28 - 7 = 21","44 - 21 = 23","23 + 4 = 27"],"target":27}}
+{"instance_id":"countdown_2k_176","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 15, 8, 4]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [8, 15, 8, 4], target: 25. Options for choosing two numbers: [(8, 15), (8, 8), (8, 4), (15, 8), (15, 4), (8, 4)].\n |- Pick two numbers (8, 15) (numbers left: [8, 4]). Try possible operations.\n  |- Try 15 + 8 = 23. Add 23 to the number set. Current number set: [23, 8, 4], target: 25. Options for choosing two numbers: [(23, 8), (23, 4), (8, 4)].\n   |- Pick two numbers (23, 8) (numbers left: [4]). Try possible operations.\n    |- Try 23 + 8 = 31. Add 31 to the number set. Current number set: [31, 4], target: 25, just two numbers left.\n     |- Try 31 + 4 = 35. Evaluate 35 != 25, drop this branch.\n     |- Try 31 - 4 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 31 * 4 = 124. Evaluate 124 != 25, drop this branch.\n     |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 23 - 8 = 15. Add 15 to the number set. Current number set: [15, 4], target: 25, just two numbers left.\n     |- Try 15 + 4 = 19. Evaluate 19 != 25, drop this branch.\n     |- Try 15 - 4 = 11. Evaluate 11 != 25, drop this branch.\n     |- Try 15 * 4 = 60. Evaluate 60 != 25, drop this branch.\n     |- Try 15 \/ 4 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 23 * 8 = 184. Add 184 to the number set. Current number set: [184, 4], target: 25, just two numbers left.\n     |- Try 184 + 4 = 188. Evaluate 188 != 25, drop this branch.\n     |- Try 184 - 4 = 180. Evaluate 180 != 25, drop this branch.\n     |- Try 184 * 4 = 736. Evaluate 736 != 25, drop this branch.\n     |- Try 184 \/ 4 = 46. Evaluate 46 != 25, drop this branch.\n    |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (23, 4) (numbers left: [8]). Try possible operations.\n    |- Try 23 + 4 = 27. Add 27 to the number set. Current number set: [27, 8], target: 25, just two numbers left.\n     |- Try 27 + 8 = 35. Evaluate 35 != 25, drop this branch.\n     |- Try 27 - 8 = 19. Evaluate 19 != 25, drop this branch.\n     |- Try 27 * 8 = 216. Evaluate 216 != 25, drop this branch.\n     |- Try 27 \/ 8 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 23 - 4 = 19. Add 19 to the number set. Current number set: [19, 8], target: 25, just two numbers left.\n     |- Try 19 + 8 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 19 - 8 = 11. Evaluate 11 != 25, drop this branch.\n     |- Try 19 * 8 = 152. Evaluate 152 != 25, drop this branch.\n     |- Try 19 \/ 8 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 23 * 4 = 92. Add 92 to the number set. Current number set: [92, 8], target: 25, just two numbers left.\n     |- Try 92 + 8 = 100. Evaluate 100 != 25, drop this branch.\n     |- Try 92 - 8 = 84. Evaluate 84 != 25, drop this branch.\n     |- Try 92 * 8 = 736. Evaluate 736 != 25, drop this branch.\n     |- Try 92 \/ 8 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 23 \/ 4 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [23]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 23], target: 25, just two numbers left.\n     |- Try 23 + 12 = 35. Evaluate 35 != 25, drop this branch.\n     |- Try 23 - 12 = 11. Evaluate 11 != 25, drop this branch.\n     |- Try 23 * 12 = 276. Evaluate 276 != 25, drop this branch.\n     |- Try 23 \/ 12 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 23], target: 25, just two numbers left.\n     |- Try 23 + 4 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 23 - 4 = 19. Evaluate 19 != 25, drop this branch.\n     |- Try 23 * 4 = 92. Evaluate 92 != 25, drop this branch.\n     |- Try 23 \/ 4 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 23], target: 25, just two numbers left.\n     |- Try 32 + 23 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 32 - 23 = 9. Evaluate 9 != 25, drop this branch.\n     |- Try 32 * 23 = 736. Evaluate 736 != 25, drop this branch.\n     |- Try 32 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 23], target: 25, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 2 = 25\nThe step before: 8 \/ 4 = 2\nThe first step: 15 + 8 = 23\n\nOutput the solution in the required format:\n<Solution>\n15 + 8 = 23\n8 \/ 4 = 2\n23 + 2 = 25\n<\/Solution>\n","item":{"nums":[8,15,8,4],"solution":["15 + 8 = 23","8 \/ 4 = 2","23 + 2 = 25"],"target":25}}
+{"instance_id":"countdown_2k_177","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 45, 18, 32]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [47, 45, 18, 32], target: 12. Options for choosing two numbers: [(47, 45), (47, 18), (47, 32), (45, 18), (45, 32), (18, 32)].\n |- Pick two numbers (47, 45) (numbers left: [18, 32]). Try possible operations.\n  |- Try 47 + 45 = 92. Add 92 to the number set. Current number set: [92, 18, 32], target: 12. Options for choosing two numbers: [(92, 18), (92, 32), (18, 32)].\n   |- Pick two numbers (92, 18) (numbers left: [32]). Try possible operations.\n    |- Try 92 + 18 = 110. Add 110 to the number set. Current number set: [110, 32], target: 12, just two numbers left.\n     |- Try 110 + 32 = 142. Evaluate 142 != 12, drop this branch.\n     |- Try 110 - 32 = 78. Evaluate 78 != 12, drop this branch.\n     |- Try 110 * 32 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 32 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 92 - 18 = 74. Add 74 to the number set. Current number set: [74, 32], target: 12, just two numbers left.\n     |- Try 74 + 32 = 106. Evaluate 106 != 12, drop this branch.\n     |- Try 74 - 32 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 74 * 32 = 2368. 2368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 32 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 92 * 18 = 1656. Add 1656 to the number set. Current number set: [1656, 32], target: 12, just two numbers left.\n     |- Try 1656 + 32 = 1688. Evaluate 1688 != 12, drop this branch.\n     |- Try 1656 - 32 = 1624. Evaluate 1624 != 12, drop this branch.\n     |- Try 1656 * 32 = 52992. 52992 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1656 \/ 32 = 51.8. 51.8 is a decimal, drop this branch.\n    |- Try 92 \/ 18 = 5.1. 5.1 is a decimal, drop this branch.\n   |- Pick two numbers (92, 32) (numbers left: [18]). Try possible operations.\n    |- Try 92 + 32 = 124. Add 124 to the number set. Current number set: [124, 18], target: 12, just two numbers left.\n     |- Try 124 + 18 = 142. Evaluate 142 != 12, drop this branch.\n     |- Try 124 - 18 = 106. Evaluate 106 != 12, drop this branch.\n     |- Try 124 * 18 = 2232. 2232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 18 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 92 - 32 = 60. Add 60 to the number set. Current number set: [60, 18], target: 12, just two numbers left.\n     |- Try 60 + 18 = 78. Evaluate 78 != 12, drop this branch.\n     |- Try 60 - 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 60 * 18 = 1080. Evaluate 1080 != 12, drop this branch.\n     |- Try 60 \/ 18 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 92 * 32 = 2944. 2944 exceeds the maximum intermediate result, drop this branch.\n    |- Try 92 \/ 32 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (18, 32) (numbers left: [92]). Try possible operations.\n    |- Try 32 + 18 = 50. Add 50 to the number set. Current number set: [50, 92], target: 12, just two numbers left.\n     |- Try 92 + 50 = 142. Evaluate 142 != 12, drop this branch.\n     |- Try 92 - 50 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 92 * 50 = 4600. 4600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 50 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 32 - 18 = 14. Add 14 to the number set. Current number set: [14, 92], target: 12, just two numbers left.\n     |- Try 92 + 14 = 106. Evaluate 106 != 12, drop this branch.\n     |- Try 92 - 14 = 78. Evaluate 78 != 12, drop this branch.\n     |- Try 92 * 14 = 1288. Evaluate 1288 != 12, drop this branch.\n     |- Try 92 \/ 14 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 32 * 18 = 576. Add 576 to the number set. Current number set: [576, 92], target: 12, just two numbers left.\n     |- Try 576 + 92 = 668. Evaluate 668 != 12, drop this branch.\n     |- Try 576 - 92 = 484. Evaluate 484 != 12, drop this branch.\n     |- Try 576 * 92 = 52992. 52992 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 92 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 32 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 47 - 45 = 2. Add 2 to the number set. Current number set: [2, 18, 32], target: 12. Options for choosing two numbers: [(2, 18), (2, 32), (18, 32)].\n   |- Pick two numbers (2, 18) (numbers left: [32]). Try possible operations.\n    |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 32], target: 12, just two numbers left.\n     |- Try 32 + 20 = 52. Evaluate 52 != 12, drop this branch.\n     |- Try 32 - 20 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 - 20 = 12\nThe step before: 18 + 2 = 20\nThe first step: 47 - 45 = 2\n\nOutput the solution in the required format:\n<Solution>\n47 - 45 = 2\n18 + 2 = 20\n32 - 20 = 12\n<\/Solution>\n","item":{"nums":[47,45,18,32],"solution":["47 - 45 = 2","18 + 2 = 20","32 - 20 = 12"],"target":12}}
+{"instance_id":"countdown_2k_178","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 22, 29, 32]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [48, 22, 29, 32], target: 29. Options for choosing two numbers: [(48, 22), (48, 29), (48, 32), (22, 29), (22, 32), (29, 32)].\n |- Pick two numbers (48, 22) (numbers left: [29, 32]). Try possible operations.\n  |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 29, 32], target: 29. Options for choosing two numbers: [(70, 29), (70, 32), (29, 32)].\n   |- Pick two numbers (70, 29) (numbers left: [32]). Try possible operations.\n    |- Try 70 + 29 = 99. Add 99 to the number set. Current number set: [99, 32], target: 29, just two numbers left.\n     |- Try 99 + 32 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 99 - 32 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 99 * 32 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 32 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 70 - 29 = 41. Add 41 to the number set. Current number set: [41, 32], target: 29, just two numbers left.\n     |- Try 41 + 32 = 73. Evaluate 73 != 29, drop this branch.\n     |- Try 41 - 32 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 41 * 32 = 1312. Evaluate 1312 != 29, drop this branch.\n     |- Try 41 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 70 * 29 = 2030. 2030 exceeds the maximum intermediate result, drop this branch.\n    |- Try 70 \/ 29 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (70, 32) (numbers left: [29]). Try possible operations.\n    |- Try 70 + 32 = 102. Add 102 to the number set. Current number set: [102, 29], target: 29, just two numbers left.\n     |- Try 102 + 29 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 102 - 29 = 73. Evaluate 73 != 29, drop this branch.\n     |- Try 102 * 29 = 2958. 2958 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 29 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 70 - 32 = 38. Add 38 to the number set. Current number set: [38, 29], target: 29, just two numbers left.\n     |- Try 38 + 29 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 38 - 29 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 38 * 29 = 1102. Evaluate 1102 != 29, drop this branch.\n     |- Try 38 \/ 29 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 70 * 32 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n    |- Try 70 \/ 32 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 32) (numbers left: [70]). Try possible operations.\n    |- Try 32 + 29 = 61. Add 61 to the number set. Current number set: [61, 70], target: 29, just two numbers left.\n     |- Try 70 + 61 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 70 - 61 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 70 * 61 = 4270. 4270 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 61 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 - 29 = 3. Add 3 to the number set. Current number set: [3, 70], target: 29, just two numbers left.\n     |- Try 70 + 3 = 73. Evaluate 73 != 29, drop this branch.\n     |- Try 70 - 3 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 70 * 3 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 70 \/ 3 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 32 * 29 = 928. Add 928 to the number set. Current number set: [928, 70], target: 29, just two numbers left.\n     |- Try 928 + 70 = 998. Evaluate 998 != 29, drop this branch.\n     |- Try 928 - 70 = 858. Evaluate 858 != 29, drop this branch.\n     |- Try 928 * 70 = 64960. 64960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 928 \/ 70 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 29, 32], target: 29. Options for choosing two numbers: [(26, 29), (26, 32), (29, 32)].\n   |- Pick two numbers (26, 29) (numbers left: [32]). Try possible operations.\n    |- Try 29 + 26 = 55. Add 55 to the number set. Current number set: [55, 32], target: 29, just two numbers left.\n     |- Try 55 + 32 = 87. Evaluate 87 != 29, drop this branch.\n     |- Try 55 - 32 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 55 * 32 = 1760. Evaluate 1760 != 29, drop this branch.\n     |- Try 55 \/ 32 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 29 - 26 = 3. Add 3 to the number set. Current number set: [3, 32], target: 29, just two numbers left.\n     |- Try 32 + 3 = 35. Evaluate 35 != 29, drop this branch.\n     |- Try 32 - 3 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 - 3 = 29\nThe step before: 29 - 26 = 3\nThe first step: 48 - 22 = 26\n\nOutput the solution in the required format:\n<Solution>\n48 - 22 = 26\n29 - 26 = 3\n32 - 3 = 29\n<\/Solution>\n","item":{"nums":[48,22,29,32],"solution":["48 - 22 = 26","29 - 26 = 3","32 - 3 = 29"],"target":29}}
+{"instance_id":"countdown_2k_179","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 27, 15, 43]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [10, 27, 15, 43], target: 11. Options for choosing two numbers: [(10, 27), (10, 15), (10, 43), (27, 15), (27, 43), (15, 43)].\n |- Pick two numbers (10, 27) (numbers left: [15, 43]). Try possible operations.\n  |- Try 27 + 10 = 37. Add 37 to the number set. Current number set: [37, 15, 43], target: 11. Options for choosing two numbers: [(37, 15), (37, 43), (15, 43)].\n   |- Pick two numbers (37, 15) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 15 = 52. Add 52 to the number set. Current number set: [52, 43], target: 11, just two numbers left.\n     |- Try 52 + 43 = 95. Evaluate 95 != 11, drop this branch.\n     |- Try 52 - 43 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 52 * 43 = 2236. 2236 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 15 = 22. Add 22 to the number set. Current number set: [22, 43], target: 11, just two numbers left.\n     |- Try 43 + 22 = 65. Evaluate 65 != 11, drop this branch.\n     |- Try 43 - 22 = 21. Evaluate 21 != 11, drop this branch.\n     |- Try 43 * 22 = 946. Evaluate 946 != 11, drop this branch.\n     |- Try 43 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 37 * 15 = 555. Add 555 to the number set. Current number set: [555, 43], target: 11, just two numbers left.\n     |- Try 555 + 43 = 598. Evaluate 598 != 11, drop this branch.\n     |- Try 555 - 43 = 512. Evaluate 512 != 11, drop this branch.\n     |- Try 555 * 43 = 23865. 23865 exceeds the maximum intermediate result, drop this branch.\n     |- Try 555 \/ 43 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 37 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (37, 43) (numbers left: [15]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 15], target: 11, just two numbers left.\n     |- Try 80 + 15 = 95. Evaluate 95 != 11, drop this branch.\n     |- Try 80 - 15 = 65. Evaluate 65 != 11, drop this branch.\n     |- Try 80 * 15 = 1200. Evaluate 1200 != 11, drop this branch.\n     |- Try 80 \/ 15 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 15], target: 11, just two numbers left.\n     |- Try 15 + 6 = 21. Evaluate 21 != 11, drop this branch.\n     |- Try 15 - 6 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 15 * 6 = 90. Evaluate 90 != 11, drop this branch.\n     |- Try 15 \/ 6 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 15], target: 11, just two numbers left.\n     |- Try 1591 + 15 = 1606. Evaluate 1606 != 11, drop this branch.\n     |- Try 1591 - 15 = 1576. Evaluate 1576 != 11, drop this branch.\n     |- Try 1591 * 15 = 23865. 23865 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 15 = 106.1. 106.1 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 43) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 15 = 58. Add 58 to the number set. Current number set: [58, 37], target: 11, just two numbers left.\n     |- Try 58 + 37 = 95. Evaluate 95 != 11, drop this branch.\n     |- Try 58 - 37 = 21. Evaluate 21 != 11, drop this branch.\n     |- Try 58 * 37 = 2146. 2146 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 43 - 15 = 28. Add 28 to the number set. Current number set: [28, 37], target: 11, just two numbers left.\n     |- Try 37 + 28 = 65. Evaluate 65 != 11, drop this branch.\n     |- Try 37 - 28 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 37 * 28 = 1036. Evaluate 1036 != 11, drop this branch.\n     |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 43 * 15 = 645. Add 645 to the number set. Current number set: [645, 37], target: 11, just two numbers left.\n     |- Try 645 + 37 = 682. Evaluate 682 != 11, drop this branch.\n     |- Try 645 - 37 = 608. Evaluate 608 != 11, drop this branch.\n     |- Try 645 * 37 = 23865. 23865 exceeds the maximum intermediate result, drop this branch.\n     |- Try 645 \/ 37 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 43 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 27 - 10 = 17. Add 17 to the number set. Current number set: [17, 15, 43], target: 11. Options for choosing two numbers: [(17, 15), (17, 43), (15, 43)].\n   |- Pick two numbers (17, 15) (numbers left: [43]). Try possible operations.\n    |- Try 17 + 15 = 32. Add 32 to the number set. Current number set: [32, 43], target: 11, just two numbers left.\n     |- Try 43 + 32 = 75. Evaluate 75 != 11, drop this branch.\n     |- Try 43 - 32 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 - 32 = 11\nThe step before: 17 + 15 = 32\nThe first step: 27 - 10 = 17\n\nOutput the solution in the required format:\n<Solution>\n27 - 10 = 17\n17 + 15 = 32\n43 - 32 = 11\n<\/Solution>\n","item":{"nums":[10,27,15,43],"solution":["27 - 10 = 17","17 + 15 = 32","43 - 32 = 11"],"target":11}}
+{"instance_id":"countdown_2k_180","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [40, 8, 28, 30]\nTarget: 34","reference_output":"# Search Procedure\nInitial number set: [40, 8, 28, 30], target: 34. Options for choosing two numbers: [(40, 8), (40, 28), (40, 30), (8, 28), (8, 30), (28, 30)].\n |- Pick two numbers (40, 8) (numbers left: [28, 30]). Try possible operations.\n  |- Try 40 + 8 = 48. Add 48 to the number set. Current number set: [48, 28, 30], target: 34. Options for choosing two numbers: [(48, 28), (48, 30), (28, 30)].\n   |- Pick two numbers (48, 28) (numbers left: [30]). Try possible operations.\n    |- Try 48 + 28 = 76. Add 76 to the number set. Current number set: [76, 30], target: 34, just two numbers left.\n     |- Try 76 + 30 = 106. Evaluate 106 != 34, drop this branch.\n     |- Try 76 - 30 = 46. Evaluate 46 != 34, drop this branch.\n     |- Try 76 * 30 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 30 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 - 28 = 20. Add 20 to the number set. Current number set: [20, 30], target: 34, just two numbers left.\n     |- Try 30 + 20 = 50. Evaluate 50 != 34, drop this branch.\n     |- Try 30 - 20 = 10. Evaluate 10 != 34, drop this branch.\n     |- Try 30 * 20 = 600. Evaluate 600 != 34, drop this branch.\n     |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 28 = 1344. Add 1344 to the number set. Current number set: [1344, 30], target: 34, just two numbers left.\n     |- Try 1344 + 30 = 1374. Evaluate 1374 != 34, drop this branch.\n     |- Try 1344 - 30 = 1314. Evaluate 1314 != 34, drop this branch.\n     |- Try 1344 * 30 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1344 \/ 30 = 44.8. 44.8 is a decimal, drop this branch.\n    |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (48, 30) (numbers left: [28]). Try possible operations.\n    |- Try 48 + 30 = 78. Add 78 to the number set. Current number set: [78, 28], target: 34, just two numbers left.\n     |- Try 78 + 28 = 106. Evaluate 106 != 34, drop this branch.\n     |- Try 78 - 28 = 50. Evaluate 50 != 34, drop this branch.\n     |- Try 78 * 28 = 2184. 2184 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 28 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 48 - 30 = 18. Add 18 to the number set. Current number set: [18, 28], target: 34, just two numbers left.\n     |- Try 28 + 18 = 46. Evaluate 46 != 34, drop this branch.\n     |- Try 28 - 18 = 10. Evaluate 10 != 34, drop this branch.\n     |- Try 28 * 18 = 504. Evaluate 504 != 34, drop this branch.\n     |- Try 28 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 48 * 30 = 1440. Add 1440 to the number set. Current number set: [1440, 28], target: 34, just two numbers left.\n     |- Try 1440 + 28 = 1468. Evaluate 1468 != 34, drop this branch.\n     |- Try 1440 - 28 = 1412. Evaluate 1412 != 34, drop this branch.\n     |- Try 1440 * 28 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1440 \/ 28 = 51.4. 51.4 is a decimal, drop this branch.\n    |- Try 48 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 30) (numbers left: [48]). Try possible operations.\n    |- Try 30 + 28 = 58. Add 58 to the number set. Current number set: [58, 48], target: 34, just two numbers left.\n     |- Try 58 + 48 = 106. Evaluate 106 != 34, drop this branch.\n     |- Try 58 - 48 = 10. Evaluate 10 != 34, drop this branch.\n     |- Try 58 * 48 = 2784. 2784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 - 28 = 2. Add 2 to the number set. Current number set: [2, 48], target: 34, just two numbers left.\n     |- Try 48 + 2 = 50. Evaluate 50 != 34, drop this branch.\n     |- Try 48 - 2 = 46. Evaluate 46 != 34, drop this branch.\n     |- Try 48 * 2 = 96. Evaluate 96 != 34, drop this branch.\n     |- Try 48 \/ 2 = 24. Evaluate 24 != 34, drop this branch.\n    |- Try 30 * 28 = 840. Add 840 to the number set. Current number set: [840, 48], target: 34, just two numbers left.\n     |- Try 840 + 48 = 888. Evaluate 888 != 34, drop this branch.\n     |- Try 840 - 48 = 792. Evaluate 792 != 34, drop this branch.\n     |- Try 840 * 48 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 48 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 30 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 40 - 8 = 32. Add 32 to the number set. Current number set: [32, 28, 30], target: 34. Options for choosing two numbers: [(32, 28), (32, 30), (28, 30)].\n   |- Pick two numbers (32, 28) (numbers left: [30]). Try possible operations.\n    |- Try 32 + 28 = 60. Add 60 to the number set. Current number set: [60, 30], target: 34, just two numbers left.\n     |- Try 60 + 30 = 90. Evaluate 90 != 34, drop this branch.\n     |- Try 60 - 30 = 30. Evaluate 30 != 34, drop this branch.\n     |- Try 60 * 30 = 1800. Evaluate 1800 != 34, drop this branch.\n     |- Try 60 \/ 30 = 2. Evaluate 2 != 34, drop this branch.\n    |- Try 32 - 28 = 4. Add 4 to the number set. Current number set: [4, 30], target: 34, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 == 34, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 + 4 = 34\nThe step before: 32 - 28 = 4\nThe first step: 40 - 8 = 32\n\nOutput the solution in the required format:\n<Solution>\n40 - 8 = 32\n32 - 28 = 4\n30 + 4 = 34\n<\/Solution>\n","item":{"nums":[40,8,28,30],"solution":["40 - 8 = 32","32 - 28 = 4","30 + 4 = 34"],"target":34}}
+{"instance_id":"countdown_2k_181","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 38, 8, 4]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [19, 38, 8, 4], target: 23. Options for choosing two numbers: [(19, 38), (19, 8), (19, 4), (38, 8), (38, 4), (8, 4)].\n |- Pick two numbers (19, 38) (numbers left: [8, 4]). Try possible operations.\n  |- Try 38 + 19 = 57. Add 57 to the number set. Current number set: [57, 8, 4], target: 23. Options for choosing two numbers: [(57, 8), (57, 4), (8, 4)].\n   |- Pick two numbers (57, 8) (numbers left: [4]). Try possible operations.\n    |- Try 57 + 8 = 65. Add 65 to the number set. Current number set: [65, 4], target: 23, just two numbers left.\n     |- Try 65 + 4 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 65 - 4 = 61. Evaluate 61 != 23, drop this branch.\n     |- Try 65 * 4 = 260. Evaluate 260 != 23, drop this branch.\n     |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 57 - 8 = 49. Add 49 to the number set. Current number set: [49, 4], target: 23, just two numbers left.\n     |- Try 49 + 4 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 49 - 4 = 45. Evaluate 45 != 23, drop this branch.\n     |- Try 49 * 4 = 196. Evaluate 196 != 23, drop this branch.\n     |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 57 * 8 = 456. Add 456 to the number set. Current number set: [456, 4], target: 23, just two numbers left.\n     |- Try 456 + 4 = 460. Evaluate 460 != 23, drop this branch.\n     |- Try 456 - 4 = 452. Evaluate 452 != 23, drop this branch.\n     |- Try 456 * 4 = 1824. Evaluate 1824 != 23, drop this branch.\n     |- Try 456 \/ 4 = 114. Evaluate 114 != 23, drop this branch.\n    |- Try 57 \/ 8 = 7.1. 7.1 is a decimal, drop this branch.\n   |- Pick two numbers (57, 4) (numbers left: [8]). Try possible operations.\n    |- Try 57 + 4 = 61. Add 61 to the number set. Current number set: [61, 8], target: 23, just two numbers left.\n     |- Try 61 + 8 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 61 - 8 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 61 * 8 = 488. Evaluate 488 != 23, drop this branch.\n     |- Try 61 \/ 8 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 57 - 4 = 53. Add 53 to the number set. Current number set: [53, 8], target: 23, just two numbers left.\n     |- Try 53 + 8 = 61. Evaluate 61 != 23, drop this branch.\n     |- Try 53 - 8 = 45. Evaluate 45 != 23, drop this branch.\n     |- Try 53 * 8 = 424. Evaluate 424 != 23, drop this branch.\n     |- Try 53 \/ 8 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 57 * 4 = 228. Add 228 to the number set. Current number set: [228, 8], target: 23, just two numbers left.\n     |- Try 228 + 8 = 236. Evaluate 236 != 23, drop this branch.\n     |- Try 228 - 8 = 220. Evaluate 220 != 23, drop this branch.\n     |- Try 228 * 8 = 1824. Evaluate 1824 != 23, drop this branch.\n     |- Try 228 \/ 8 = 28.5. 28.5 is a decimal, drop this branch.\n    |- Try 57 \/ 4 = 14.2. 14.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [57]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 57], target: 23, just two numbers left.\n     |- Try 57 + 12 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 57 - 12 = 45. Evaluate 45 != 23, drop this branch.\n     |- Try 57 * 12 = 684. Evaluate 684 != 23, drop this branch.\n     |- Try 57 \/ 12 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 57], target: 23, just two numbers left.\n     |- Try 57 + 4 = 61. Evaluate 61 != 23, drop this branch.\n     |- Try 57 - 4 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 57 * 4 = 228. Evaluate 228 != 23, drop this branch.\n     |- Try 57 \/ 4 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 57], target: 23, just two numbers left.\n     |- Try 57 + 32 = 89. Evaluate 89 != 23, drop this branch.\n     |- Try 57 - 32 = 25. Evaluate 25 != 23, drop this branch.\n     |- Try 57 * 32 = 1824. Evaluate 1824 != 23, drop this branch.\n     |- Try 57 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 57], target: 23, just two numbers left.\n     |- Try 57 + 2 = 59. Evaluate 59 != 23, drop this branch.\n     |- Try 57 - 2 = 55. Evaluate 55 != 23, drop this branch.\n     |- Try 57 * 2 = 114. Evaluate 114 != 23, drop this branch.\n     |- Try 57 \/ 2 = 28.5. 28.5 is a decimal, drop this branch.\n  |- Try 38 - 19 = 19. Add 19 to the number set. Current number set: [19, 8, 4], target: 23. Options for choosing two numbers: [(19, 8), (19, 4), (8, 4)].\n   |- Pick two numbers (19, 8) (numbers left: [4]). Try possible operations.\n    |- Try 19 + 8 = 27. Add 27 to the number set. Current number set: [27, 4], target: 23, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 23, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 - 4 = 23\nThe step before: 19 + 8 = 27\nThe first step: 38 - 19 = 19\n\nOutput the solution in the required format:\n<Solution>\n38 - 19 = 19\n19 + 8 = 27\n27 - 4 = 23\n<\/Solution>\n","item":{"nums":[19,38,8,4],"solution":["38 - 19 = 19","19 + 8 = 27","27 - 4 = 23"],"target":23}}
+{"instance_id":"countdown_2k_182","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 28, 44, 21]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [37, 28, 44, 21], target: 32. Options for choosing two numbers: [(37, 28), (37, 44), (37, 21), (28, 44), (28, 21), (44, 21)].\n |- Pick two numbers (37, 28) (numbers left: [44, 21]). Try possible operations.\n  |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 44, 21], target: 32. Options for choosing two numbers: [(65, 44), (65, 21), (44, 21)].\n   |- Pick two numbers (65, 44) (numbers left: [21]). Try possible operations.\n    |- Try 65 + 44 = 109. Add 109 to the number set. Current number set: [109, 21], target: 32, just two numbers left.\n     |- Try 109 + 21 = 130. Evaluate 130 != 32, drop this branch.\n     |- Try 109 - 21 = 88. Evaluate 88 != 32, drop this branch.\n     |- Try 109 * 21 = 2289. 2289 exceeds the maximum intermediate result, drop this branch.\n     |- Try 109 \/ 21 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 65 - 44 = 21. Add 21 to the number set. Current number set: [21, 21], target: 32, just two numbers left.\n     |- Try 21 + 21 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 21 - 21 = 0. Evaluate 0 != 32, drop this branch.\n     |- Try 21 * 21 = 441. Evaluate 441 != 32, drop this branch.\n     |- Try 21 \/ 21 = 1. Evaluate 1 != 32, drop this branch.\n    |- Try 65 * 44 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n    |- Try 65 \/ 44 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (65, 21) (numbers left: [44]). Try possible operations.\n    |- Try 65 + 21 = 86. Add 86 to the number set. Current number set: [86, 44], target: 32, just two numbers left.\n     |- Try 86 + 44 = 130. Evaluate 130 != 32, drop this branch.\n     |- Try 86 - 44 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 86 * 44 = 3784. 3784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 44 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 65 - 21 = 44. Add 44 to the number set. Current number set: [44, 44], target: 32, just two numbers left.\n     |- Try 44 + 44 = 88. Evaluate 88 != 32, drop this branch.\n     |- Try 44 - 44 = 0. Evaluate 0 != 32, drop this branch.\n     |- Try 44 * 44 = 1936. Evaluate 1936 != 32, drop this branch.\n     |- Try 44 \/ 44 = 1. Evaluate 1 != 32, drop this branch.\n    |- Try 65 * 21 = 1365. Add 1365 to the number set. Current number set: [1365, 44], target: 32, just two numbers left.\n     |- Try 1365 + 44 = 1409. Evaluate 1409 != 32, drop this branch.\n     |- Try 1365 - 44 = 1321. Evaluate 1321 != 32, drop this branch.\n     |- Try 1365 * 44 = 60060. 60060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1365 \/ 44 = 31.0. 31.0 is a decimal, drop this branch.\n    |- Try 65 \/ 21 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (44, 21) (numbers left: [65]). Try possible operations.\n    |- Try 44 + 21 = 65. Add 65 to the number set. Current number set: [65, 65], target: 32, just two numbers left.\n     |- Try 65 + 65 = 130. Evaluate 130 != 32, drop this branch.\n     |- Try 65 - 65 = 0. Evaluate 0 != 32, drop this branch.\n     |- Try 65 * 65 = 4225. 4225 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 65 = 1. Evaluate 1 != 32, drop this branch.\n    |- Try 44 - 21 = 23. Add 23 to the number set. Current number set: [23, 65], target: 32, just two numbers left.\n     |- Try 65 + 23 = 88. Evaluate 88 != 32, drop this branch.\n     |- Try 65 - 23 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 65 * 23 = 1495. Evaluate 1495 != 32, drop this branch.\n     |- Try 65 \/ 23 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 44 * 21 = 924. Add 924 to the number set. Current number set: [924, 65], target: 32, just two numbers left.\n     |- Try 924 + 65 = 989. Evaluate 989 != 32, drop this branch.\n     |- Try 924 - 65 = 859. Evaluate 859 != 32, drop this branch.\n     |- Try 924 * 65 = 60060. 60060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 65 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 44 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 44, 21], target: 32. Options for choosing two numbers: [(9, 44), (9, 21), (44, 21)].\n   |- Pick two numbers (9, 44) (numbers left: [21]). Try possible operations.\n    |- Try 44 + 9 = 53. Add 53 to the number set. Current number set: [53, 21], target: 32, just two numbers left.\n     |- Try 53 + 21 = 74. Evaluate 74 != 32, drop this branch.\n     |- Try 53 - 21 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 53 - 21 = 32\nThe step before: 44 + 9 = 53\nThe first step: 37 - 28 = 9\n\nOutput the solution in the required format:\n<Solution>\n37 - 28 = 9\n44 + 9 = 53\n53 - 21 = 32\n<\/Solution>\n","item":{"nums":[37,28,44,21],"solution":["37 - 28 = 9","44 + 9 = 53","53 - 21 = 32"],"target":32}}
+{"instance_id":"countdown_2k_183","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 48, 43, 16]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [10, 48, 43, 16], target: 21. Options for choosing two numbers: [(10, 48), (10, 43), (10, 16), (48, 43), (48, 16), (43, 16)].\n |- Pick two numbers (10, 48) (numbers left: [43, 16]). Try possible operations.\n  |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 43, 16], target: 21. Options for choosing two numbers: [(58, 43), (58, 16), (43, 16)].\n   |- Pick two numbers (58, 43) (numbers left: [16]). Try possible operations.\n    |- Try 58 + 43 = 101. Add 101 to the number set. Current number set: [101, 16], target: 21, just two numbers left.\n     |- Try 101 + 16 = 117. Evaluate 117 != 21, drop this branch.\n     |- Try 101 - 16 = 85. Evaluate 85 != 21, drop this branch.\n     |- Try 101 * 16 = 1616. Evaluate 1616 != 21, drop this branch.\n     |- Try 101 \/ 16 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 58 - 43 = 15. Add 15 to the number set. Current number set: [15, 16], target: 21, just two numbers left.\n     |- Try 16 + 15 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 16 - 15 = 1. Evaluate 1 != 21, drop this branch.\n     |- Try 16 * 15 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 16 \/ 15 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 58 * 43 = 2494. 2494 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 43 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (58, 16) (numbers left: [43]). Try possible operations.\n    |- Try 58 + 16 = 74. Add 74 to the number set. Current number set: [74, 43], target: 21, just two numbers left.\n     |- Try 74 + 43 = 117. Evaluate 117 != 21, drop this branch.\n     |- Try 74 - 43 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 74 * 43 = 3182. 3182 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 43 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 58 - 16 = 42. Add 42 to the number set. Current number set: [42, 43], target: 21, just two numbers left.\n     |- Try 43 + 42 = 85. Evaluate 85 != 21, drop this branch.\n     |- Try 43 - 42 = 1. Evaluate 1 != 21, drop this branch.\n     |- Try 43 * 42 = 1806. Evaluate 1806 != 21, drop this branch.\n     |- Try 43 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 58 * 16 = 928. Add 928 to the number set. Current number set: [928, 43], target: 21, just two numbers left.\n     |- Try 928 + 43 = 971. Evaluate 971 != 21, drop this branch.\n     |- Try 928 - 43 = 885. Evaluate 885 != 21, drop this branch.\n     |- Try 928 * 43 = 39904. 39904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 928 \/ 43 = 21.6. 21.6 is a decimal, drop this branch.\n    |- Try 58 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (43, 16) (numbers left: [58]). Try possible operations.\n    |- Try 43 + 16 = 59. Add 59 to the number set. Current number set: [59, 58], target: 21, just two numbers left.\n     |- Try 59 + 58 = 117. Evaluate 117 != 21, drop this branch.\n     |- Try 59 - 58 = 1. Evaluate 1 != 21, drop this branch.\n     |- Try 59 * 58 = 3422. 3422 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 58 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 43 - 16 = 27. Add 27 to the number set. Current number set: [27, 58], target: 21, just two numbers left.\n     |- Try 58 + 27 = 85. Evaluate 85 != 21, drop this branch.\n     |- Try 58 - 27 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 58 * 27 = 1566. Evaluate 1566 != 21, drop this branch.\n     |- Try 58 \/ 27 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 43 * 16 = 688. Add 688 to the number set. Current number set: [688, 58], target: 21, just two numbers left.\n     |- Try 688 + 58 = 746. Evaluate 746 != 21, drop this branch.\n     |- Try 688 - 58 = 630. Evaluate 630 != 21, drop this branch.\n     |- Try 688 * 58 = 39904. 39904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 688 \/ 58 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 43 \/ 16 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 48 - 10 = 38. Add 38 to the number set. Current number set: [38, 43, 16], target: 21. Options for choosing two numbers: [(38, 43), (38, 16), (43, 16)].\n   |- Pick two numbers (38, 43) (numbers left: [16]). Try possible operations.\n    |- Try 43 + 38 = 81. Add 81 to the number set. Current number set: [81, 16], target: 21, just two numbers left.\n     |- Try 81 + 16 = 97. Evaluate 97 != 21, drop this branch.\n     |- Try 81 - 16 = 65. Evaluate 65 != 21, drop this branch.\n     |- Try 81 * 16 = 1296. Evaluate 1296 != 21, drop this branch.\n     |- Try 81 \/ 16 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 43 - 38 = 5. Add 5 to the number set. Current number set: [5, 16], target: 21, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 5 = 21\nThe step before: 43 - 38 = 5\nThe first step: 48 - 10 = 38\n\nOutput the solution in the required format:\n<Solution>\n48 - 10 = 38\n43 - 38 = 5\n16 + 5 = 21\n<\/Solution>\n","item":{"nums":[10,48,43,16],"solution":["48 - 10 = 38","43 - 38 = 5","16 + 5 = 21"],"target":21}}
+{"instance_id":"countdown_2k_184","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 28, 4, 16]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [22, 28, 4, 16], target: 18. Options for choosing two numbers: [(22, 28), (22, 4), (22, 16), (28, 4), (28, 16), (4, 16)].\n |- Pick two numbers (22, 28) (numbers left: [4, 16]). Try possible operations.\n  |- Try 28 + 22 = 50. Add 50 to the number set. Current number set: [50, 4, 16], target: 18. Options for choosing two numbers: [(50, 4), (50, 16), (4, 16)].\n   |- Pick two numbers (50, 4) (numbers left: [16]). Try possible operations.\n    |- Try 50 + 4 = 54. Add 54 to the number set. Current number set: [54, 16], target: 18, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 18, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 18, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 18, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 50 - 4 = 46. Add 46 to the number set. Current number set: [46, 16], target: 18, just two numbers left.\n     |- Try 46 + 16 = 62. Evaluate 62 != 18, drop this branch.\n     |- Try 46 - 16 = 30. Evaluate 30 != 18, drop this branch.\n     |- Try 46 * 16 = 736. Evaluate 736 != 18, drop this branch.\n     |- Try 46 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 50 * 4 = 200. Add 200 to the number set. Current number set: [200, 16], target: 18, just two numbers left.\n     |- Try 200 + 16 = 216. Evaluate 216 != 18, drop this branch.\n     |- Try 200 - 16 = 184. Evaluate 184 != 18, drop this branch.\n     |- Try 200 * 16 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 200 \/ 16 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 50 \/ 4 = 12.5. 12.5 is a decimal, drop this branch.\n   |- Pick two numbers (50, 16) (numbers left: [4]). Try possible operations.\n    |- Try 50 + 16 = 66. Add 66 to the number set. Current number set: [66, 4], target: 18, just two numbers left.\n     |- Try 66 + 4 = 70. Evaluate 70 != 18, drop this branch.\n     |- Try 66 - 4 = 62. Evaluate 62 != 18, drop this branch.\n     |- Try 66 * 4 = 264. Evaluate 264 != 18, drop this branch.\n     |- Try 66 \/ 4 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 50 - 16 = 34. Add 34 to the number set. Current number set: [34, 4], target: 18, just two numbers left.\n     |- Try 34 + 4 = 38. Evaluate 38 != 18, drop this branch.\n     |- Try 34 - 4 = 30. Evaluate 30 != 18, drop this branch.\n     |- Try 34 * 4 = 136. Evaluate 136 != 18, drop this branch.\n     |- Try 34 \/ 4 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 50 * 16 = 800. Add 800 to the number set. Current number set: [800, 4], target: 18, just two numbers left.\n     |- Try 800 + 4 = 804. Evaluate 804 != 18, drop this branch.\n     |- Try 800 - 4 = 796. Evaluate 796 != 18, drop this branch.\n     |- Try 800 * 4 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 4 = 200. Evaluate 200 != 18, drop this branch.\n    |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (4, 16) (numbers left: [50]). Try possible operations.\n    |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 50], target: 18, just two numbers left.\n     |- Try 50 + 20 = 70. Evaluate 70 != 18, drop this branch.\n     |- Try 50 - 20 = 30. Evaluate 30 != 18, drop this branch.\n     |- Try 50 * 20 = 1000. Evaluate 1000 != 18, drop this branch.\n     |- Try 50 \/ 20 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 50], target: 18, just two numbers left.\n     |- Try 50 + 12 = 62. Evaluate 62 != 18, drop this branch.\n     |- Try 50 - 12 = 38. Evaluate 38 != 18, drop this branch.\n     |- Try 50 * 12 = 600. Evaluate 600 != 18, drop this branch.\n     |- Try 50 \/ 12 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 16 * 4 = 64. Add 64 to the number set. Current number set: [64, 50], target: 18, just two numbers left.\n     |- Try 64 + 50 = 114. Evaluate 114 != 18, drop this branch.\n     |- Try 64 - 50 = 14. Evaluate 14 != 18, drop this branch.\n     |- Try 64 * 50 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 50 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 16 \/ 4 = 4. Add 4 to the number set. Current number set: [4, 50], target: 18, just two numbers left.\n     |- Try 50 + 4 = 54. Evaluate 54 != 18, drop this branch.\n     |- Try 50 - 4 = 46. Evaluate 46 != 18, drop this branch.\n     |- Try 50 * 4 = 200. Evaluate 200 != 18, drop this branch.\n     |- Try 50 \/ 4 = 12.5. 12.5 is a decimal, drop this branch.\n  |- Try 28 - 22 = 6. Add 6 to the number set. Current number set: [6, 4, 16], target: 18. Options for choosing two numbers: [(6, 4), (6, 16), (4, 16)].\n   |- Pick two numbers (6, 4) (numbers left: [16]). Try possible operations.\n    |- Try 6 + 4 = 10. Add 10 to the number set. Current number set: [10, 16], target: 18, just two numbers left.\n     |- Try 16 + 10 = 26. Evaluate 26 != 18, drop this branch.\n     |- Try 16 - 10 = 6. Evaluate 6 != 18, drop this branch.\n     |- Try 16 * 10 = 160. Evaluate 160 != 18, drop this branch.\n     |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 6 - 4 = 2. Add 2 to the number set. Current number set: [2, 16], target: 18, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 2 = 18\nThe step before: 6 - 4 = 2\nThe first step: 28 - 22 = 6\n\nOutput the solution in the required format:\n<Solution>\n28 - 22 = 6\n6 - 4 = 2\n16 + 2 = 18\n<\/Solution>\n","item":{"nums":[22,28,4,16],"solution":["28 - 22 = 6","6 - 4 = 2","16 + 2 = 18"],"target":18}}
+{"instance_id":"countdown_2k_185","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [40, 25, 32, 2]\nTarget: 34","reference_output":"# Search Procedure\nInitial number set: [40, 25, 32, 2], target: 34. Options for choosing two numbers: [(40, 25), (40, 32), (40, 2), (25, 32), (25, 2), (32, 2)].\n |- Pick two numbers (40, 25) (numbers left: [32, 2]). Try possible operations.\n  |- Try 40 + 25 = 65. Add 65 to the number set. Current number set: [65, 32, 2], target: 34. Options for choosing two numbers: [(65, 32), (65, 2), (32, 2)].\n   |- Pick two numbers (65, 32) (numbers left: [2]). Try possible operations.\n    |- Try 65 + 32 = 97. Add 97 to the number set. Current number set: [97, 2], target: 34, just two numbers left.\n     |- Try 97 + 2 = 99. Evaluate 99 != 34, drop this branch.\n     |- Try 97 - 2 = 95. Evaluate 95 != 34, drop this branch.\n     |- Try 97 * 2 = 194. Evaluate 194 != 34, drop this branch.\n     |- Try 97 \/ 2 = 48.5. 48.5 is a decimal, drop this branch.\n    |- Try 65 - 32 = 33. Add 33 to the number set. Current number set: [33, 2], target: 34, just two numbers left.\n     |- Try 33 + 2 = 35. Evaluate 35 != 34, drop this branch.\n     |- Try 33 - 2 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 33 * 2 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 65 * 32 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n    |- Try 65 \/ 32 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (65, 2) (numbers left: [32]). Try possible operations.\n    |- Try 65 + 2 = 67. Add 67 to the number set. Current number set: [67, 32], target: 34, just two numbers left.\n     |- Try 67 + 32 = 99. Evaluate 99 != 34, drop this branch.\n     |- Try 67 - 32 = 35. Evaluate 35 != 34, drop this branch.\n     |- Try 67 * 32 = 2144. 2144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 32 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 65 - 2 = 63. Add 63 to the number set. Current number set: [63, 32], target: 34, just two numbers left.\n     |- Try 63 + 32 = 95. Evaluate 95 != 34, drop this branch.\n     |- Try 63 - 32 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 63 * 32 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 32 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 65 * 2 = 130. Add 130 to the number set. Current number set: [130, 32], target: 34, just two numbers left.\n     |- Try 130 + 32 = 162. Evaluate 162 != 34, drop this branch.\n     |- Try 130 - 32 = 98. Evaluate 98 != 34, drop this branch.\n     |- Try 130 * 32 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 32 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 65 \/ 2 = 32.5. 32.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [65]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 65], target: 34, just two numbers left.\n     |- Try 65 + 34 = 99. Evaluate 99 != 34, drop this branch.\n     |- Try 65 - 34 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 65 * 34 = 2210. 2210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 34 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 65], target: 34, just two numbers left.\n     |- Try 65 + 30 = 95. Evaluate 95 != 34, drop this branch.\n     |- Try 65 - 30 = 35. Evaluate 35 != 34, drop this branch.\n     |- Try 65 * 30 = 1950. Evaluate 1950 != 34, drop this branch.\n     |- Try 65 \/ 30 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 65], target: 34, just two numbers left.\n     |- Try 65 + 64 = 129. Evaluate 129 != 34, drop this branch.\n     |- Try 65 - 64 = 1. Evaluate 1 != 34, drop this branch.\n     |- Try 65 * 64 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 64 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 65], target: 34, just two numbers left.\n     |- Try 65 + 16 = 81. Evaluate 81 != 34, drop this branch.\n     |- Try 65 - 16 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 65 * 16 = 1040. Evaluate 1040 != 34, drop this branch.\n     |- Try 65 \/ 16 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 40 - 25 = 15. Add 15 to the number set. Current number set: [15, 32, 2], target: 34. Options for choosing two numbers: [(15, 32), (15, 2), (32, 2)].\n   |- Pick two numbers (15, 32) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 15 = 47. Add 47 to the number set. Current number set: [47, 2], target: 34, just two numbers left.\n     |- Try 47 + 2 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 47 - 2 = 45. Evaluate 45 != 34, drop this branch.\n     |- Try 47 * 2 = 94. Evaluate 94 != 34, drop this branch.\n     |- Try 47 \/ 2 = 23.5. 23.5 is a decimal, drop this branch.\n    |- Try 32 - 15 = 17. Add 17 to the number set. Current number set: [17, 2], target: 34, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 34, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 34, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 == 34, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 17 * 2 = 34\nThe step before: 32 - 15 = 17\nThe first step: 40 - 25 = 15\n\nOutput the solution in the required format:\n<Solution>\n40 - 25 = 15\n32 - 15 = 17\n17 * 2 = 34\n<\/Solution>\n","item":{"nums":[40,25,32,2],"solution":["40 - 25 = 15","32 - 15 = 17","17 * 2 = 34"],"target":34}}
+{"instance_id":"countdown_2k_186","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 36, 33, 5]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [23, 36, 33, 5], target: 15. Options for choosing two numbers: [(23, 36), (23, 33), (23, 5), (36, 33), (36, 5), (33, 5)].\n |- Pick two numbers (23, 36) (numbers left: [33, 5]). Try possible operations.\n  |- Try 36 + 23 = 59. Add 59 to the number set. Current number set: [59, 33, 5], target: 15. Options for choosing two numbers: [(59, 33), (59, 5), (33, 5)].\n   |- Pick two numbers (59, 33) (numbers left: [5]). Try possible operations.\n    |- Try 59 + 33 = 92. Add 92 to the number set. Current number set: [92, 5], target: 15, just two numbers left.\n     |- Try 92 + 5 = 97. Evaluate 97 != 15, drop this branch.\n     |- Try 92 - 5 = 87. Evaluate 87 != 15, drop this branch.\n     |- Try 92 * 5 = 460. Evaluate 460 != 15, drop this branch.\n     |- Try 92 \/ 5 = 18.4. 18.4 is a decimal, drop this branch.\n    |- Try 59 - 33 = 26. Add 26 to the number set. Current number set: [26, 5], target: 15, just two numbers left.\n     |- Try 26 + 5 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 26 - 5 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 26 * 5 = 130. Evaluate 130 != 15, drop this branch.\n     |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 59 * 33 = 1947. Add 1947 to the number set. Current number set: [1947, 5], target: 15, just two numbers left.\n     |- Try 1947 + 5 = 1952. Evaluate 1952 != 15, drop this branch.\n     |- Try 1947 - 5 = 1942. Evaluate 1942 != 15, drop this branch.\n     |- Try 1947 * 5 = 9735. 9735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1947 \/ 5 = 389.4. 389.4 is a decimal, drop this branch.\n    |- Try 59 \/ 33 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (59, 5) (numbers left: [33]). Try possible operations.\n    |- Try 59 + 5 = 64. Add 64 to the number set. Current number set: [64, 33], target: 15, just two numbers left.\n     |- Try 64 + 33 = 97. Evaluate 97 != 15, drop this branch.\n     |- Try 64 - 33 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 64 * 33 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 33 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 59 - 5 = 54. Add 54 to the number set. Current number set: [54, 33], target: 15, just two numbers left.\n     |- Try 54 + 33 = 87. Evaluate 87 != 15, drop this branch.\n     |- Try 54 - 33 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 54 * 33 = 1782. Evaluate 1782 != 15, drop this branch.\n     |- Try 54 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 59 * 5 = 295. Add 295 to the number set. Current number set: [295, 33], target: 15, just two numbers left.\n     |- Try 295 + 33 = 328. Evaluate 328 != 15, drop this branch.\n     |- Try 295 - 33 = 262. Evaluate 262 != 15, drop this branch.\n     |- Try 295 * 33 = 9735. 9735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 295 \/ 33 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 59 \/ 5 = 11.8. 11.8 is a decimal, drop this branch.\n   |- Pick two numbers (33, 5) (numbers left: [59]). Try possible operations.\n    |- Try 33 + 5 = 38. Add 38 to the number set. Current number set: [38, 59], target: 15, just two numbers left.\n     |- Try 59 + 38 = 97. Evaluate 97 != 15, drop this branch.\n     |- Try 59 - 38 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 59 * 38 = 2242. 2242 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 33 - 5 = 28. Add 28 to the number set. Current number set: [28, 59], target: 15, just two numbers left.\n     |- Try 59 + 28 = 87. Evaluate 87 != 15, drop this branch.\n     |- Try 59 - 28 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 59 * 28 = 1652. Evaluate 1652 != 15, drop this branch.\n     |- Try 59 \/ 28 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 * 5 = 165. Add 165 to the number set. Current number set: [165, 59], target: 15, just two numbers left.\n     |- Try 165 + 59 = 224. Evaluate 224 != 15, drop this branch.\n     |- Try 165 - 59 = 106. Evaluate 106 != 15, drop this branch.\n     |- Try 165 * 59 = 9735. 9735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 165 \/ 59 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 33 \/ 5 = 6.6. 6.6 is a decimal, drop this branch.\n  |- Try 36 - 23 = 13. Add 13 to the number set. Current number set: [13, 33, 5], target: 15. Options for choosing two numbers: [(13, 33), (13, 5), (33, 5)].\n   |- Pick two numbers (13, 33) (numbers left: [5]). Try possible operations.\n    |- Try 33 + 13 = 46. Add 46 to the number set. Current number set: [46, 5], target: 15, just two numbers left.\n     |- Try 46 + 5 = 51. Evaluate 51 != 15, drop this branch.\n     |- Try 46 - 5 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 46 * 5 = 230. Evaluate 230 != 15, drop this branch.\n     |- Try 46 \/ 5 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 33 - 13 = 20. Add 20 to the number set. Current number set: [20, 5], target: 15, just two numbers left.\n     |- Try 20 + 5 = 25. Evaluate 25 != 15, drop this branch.\n     |- Try 20 - 5 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 - 5 = 15\nThe step before: 33 - 13 = 20\nThe first step: 36 - 23 = 13\n\nOutput the solution in the required format:\n<Solution>\n36 - 23 = 13\n33 - 13 = 20\n20 - 5 = 15\n<\/Solution>\n","item":{"nums":[23,36,33,5],"solution":["36 - 23 = 13","33 - 13 = 20","20 - 5 = 15"],"target":15}}
+{"instance_id":"countdown_2k_187","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 38, 18, 7]\nTarget: 34","reference_output":"# Search Procedure\nInitial number set: [47, 38, 18, 7], target: 34. Options for choosing two numbers: [(47, 38), (47, 18), (47, 7), (38, 18), (38, 7), (18, 7)].\n |- Pick two numbers (47, 38) (numbers left: [18, 7]). Try possible operations.\n  |- Try 47 + 38 = 85. Add 85 to the number set. Current number set: [85, 18, 7], target: 34. Options for choosing two numbers: [(85, 18), (85, 7), (18, 7)].\n   |- Pick two numbers (85, 18) (numbers left: [7]). Try possible operations.\n    |- Try 85 + 18 = 103. Add 103 to the number set. Current number set: [103, 7], target: 34, just two numbers left.\n     |- Try 103 + 7 = 110. Evaluate 110 != 34, drop this branch.\n     |- Try 103 - 7 = 96. Evaluate 96 != 34, drop this branch.\n     |- Try 103 * 7 = 721. Evaluate 721 != 34, drop this branch.\n     |- Try 103 \/ 7 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 85 - 18 = 67. Add 67 to the number set. Current number set: [67, 7], target: 34, just two numbers left.\n     |- Try 67 + 7 = 74. Evaluate 74 != 34, drop this branch.\n     |- Try 67 - 7 = 60. Evaluate 60 != 34, drop this branch.\n     |- Try 67 * 7 = 469. Evaluate 469 != 34, drop this branch.\n     |- Try 67 \/ 7 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 85 * 18 = 1530. Add 1530 to the number set. Current number set: [1530, 7], target: 34, just two numbers left.\n     |- Try 1530 + 7 = 1537. Evaluate 1537 != 34, drop this branch.\n     |- Try 1530 - 7 = 1523. Evaluate 1523 != 34, drop this branch.\n     |- Try 1530 * 7 = 10710. 10710 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1530 \/ 7 = 218.6. 218.6 is a decimal, drop this branch.\n    |- Try 85 \/ 18 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (85, 7) (numbers left: [18]). Try possible operations.\n    |- Try 85 + 7 = 92. Add 92 to the number set. Current number set: [92, 18], target: 34, just two numbers left.\n     |- Try 92 + 18 = 110. Evaluate 110 != 34, drop this branch.\n     |- Try 92 - 18 = 74. Evaluate 74 != 34, drop this branch.\n     |- Try 92 * 18 = 1656. Evaluate 1656 != 34, drop this branch.\n     |- Try 92 \/ 18 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 85 - 7 = 78. Add 78 to the number set. Current number set: [78, 18], target: 34, just two numbers left.\n     |- Try 78 + 18 = 96. Evaluate 96 != 34, drop this branch.\n     |- Try 78 - 18 = 60. Evaluate 60 != 34, drop this branch.\n     |- Try 78 * 18 = 1404. Evaluate 1404 != 34, drop this branch.\n     |- Try 78 \/ 18 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 85 * 7 = 595. Add 595 to the number set. Current number set: [595, 18], target: 34, just two numbers left.\n     |- Try 595 + 18 = 613. Evaluate 613 != 34, drop this branch.\n     |- Try 595 - 18 = 577. Evaluate 577 != 34, drop this branch.\n     |- Try 595 * 18 = 10710. 10710 exceeds the maximum intermediate result, drop this branch.\n     |- Try 595 \/ 18 = 33.1. 33.1 is a decimal, drop this branch.\n    |- Try 85 \/ 7 = 12.1. 12.1 is a decimal, drop this branch.\n   |- Pick two numbers (18, 7) (numbers left: [85]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 85], target: 34, just two numbers left.\n     |- Try 85 + 25 = 110. Evaluate 110 != 34, drop this branch.\n     |- Try 85 - 25 = 60. Evaluate 60 != 34, drop this branch.\n     |- Try 85 * 25 = 2125. 2125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 25 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 85], target: 34, just two numbers left.\n     |- Try 85 + 11 = 96. Evaluate 96 != 34, drop this branch.\n     |- Try 85 - 11 = 74. Evaluate 74 != 34, drop this branch.\n     |- Try 85 * 11 = 935. Evaluate 935 != 34, drop this branch.\n     |- Try 85 \/ 11 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 85], target: 34, just two numbers left.\n     |- Try 126 + 85 = 211. Evaluate 211 != 34, drop this branch.\n     |- Try 126 - 85 = 41. Evaluate 41 != 34, drop this branch.\n     |- Try 126 * 85 = 10710. 10710 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 85 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 47 - 38 = 9. Add 9 to the number set. Current number set: [9, 18, 7], target: 34. Options for choosing two numbers: [(9, 18), (9, 7), (18, 7)].\n   |- Pick two numbers (9, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 7], target: 34, just two numbers left.\n     |- Try 27 + 7 = 34. Evaluate 34 == 34, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 7 = 34\nThe step before: 18 + 9 = 27\nThe first step: 47 - 38 = 9\n\nOutput the solution in the required format:\n<Solution>\n47 - 38 = 9\n18 + 9 = 27\n27 + 7 = 34\n<\/Solution>\n","item":{"nums":[47,38,18,7],"solution":["47 - 38 = 9","18 + 9 = 27","27 + 7 = 34"],"target":34}}
+{"instance_id":"countdown_2k_188","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 29, 28, 32]\nTarget: 39","reference_output":"# Search Procedure\nInitial number set: [8, 29, 28, 32], target: 39. Options for choosing two numbers: [(8, 29), (8, 28), (8, 32), (29, 28), (29, 32), (28, 32)].\n |- Pick two numbers (8, 29) (numbers left: [28, 32]). Try possible operations.\n  |- Try 29 + 8 = 37. Add 37 to the number set. Current number set: [37, 28, 32], target: 39. Options for choosing two numbers: [(37, 28), (37, 32), (28, 32)].\n   |- Pick two numbers (37, 28) (numbers left: [32]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 32], target: 39, just two numbers left.\n     |- Try 65 + 32 = 97. Evaluate 97 != 39, drop this branch.\n     |- Try 65 - 32 = 33. Evaluate 33 != 39, drop this branch.\n     |- Try 65 * 32 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 32 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 32], target: 39, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 39, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 39, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 39, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 32], target: 39, just two numbers left.\n     |- Try 1036 + 32 = 1068. Evaluate 1068 != 39, drop this branch.\n     |- Try 1036 - 32 = 1004. Evaluate 1004 != 39, drop this branch.\n     |- Try 1036 * 32 = 33152. 33152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 32 = 32.4. 32.4 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (37, 32) (numbers left: [28]). Try possible operations.\n    |- Try 37 + 32 = 69. Add 69 to the number set. Current number set: [69, 28], target: 39, just two numbers left.\n     |- Try 69 + 28 = 97. Evaluate 97 != 39, drop this branch.\n     |- Try 69 - 28 = 41. Evaluate 41 != 39, drop this branch.\n     |- Try 69 * 28 = 1932. Evaluate 1932 != 39, drop this branch.\n     |- Try 69 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 37 - 32 = 5. Add 5 to the number set. Current number set: [5, 28], target: 39, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 39, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 39, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 39, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 37 * 32 = 1184. Add 1184 to the number set. Current number set: [1184, 28], target: 39, just two numbers left.\n     |- Try 1184 + 28 = 1212. Evaluate 1212 != 39, drop this branch.\n     |- Try 1184 - 28 = 1156. Evaluate 1156 != 39, drop this branch.\n     |- Try 1184 * 28 = 33152. 33152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1184 \/ 28 = 42.3. 42.3 is a decimal, drop this branch.\n    |- Try 37 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (28, 32) (numbers left: [37]). Try possible operations.\n    |- Try 32 + 28 = 60. Add 60 to the number set. Current number set: [60, 37], target: 39, just two numbers left.\n     |- Try 60 + 37 = 97. Evaluate 97 != 39, drop this branch.\n     |- Try 60 - 37 = 23. Evaluate 23 != 39, drop this branch.\n     |- Try 60 * 37 = 2220. 2220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 32 - 28 = 4. Add 4 to the number set. Current number set: [4, 37], target: 39, just two numbers left.\n     |- Try 37 + 4 = 41. Evaluate 41 != 39, drop this branch.\n     |- Try 37 - 4 = 33. Evaluate 33 != 39, drop this branch.\n     |- Try 37 * 4 = 148. Evaluate 148 != 39, drop this branch.\n     |- Try 37 \/ 4 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 32 * 28 = 896. Add 896 to the number set. Current number set: [896, 37], target: 39, just two numbers left.\n     |- Try 896 + 37 = 933. Evaluate 933 != 39, drop this branch.\n     |- Try 896 - 37 = 859. Evaluate 859 != 39, drop this branch.\n     |- Try 896 * 37 = 33152. 33152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 896 \/ 37 = 24.2. 24.2 is a decimal, drop this branch.\n    |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 29 - 8 = 21. Add 21 to the number set. Current number set: [21, 28, 32], target: 39. Options for choosing two numbers: [(21, 28), (21, 32), (28, 32)].\n   |- Pick two numbers (21, 28) (numbers left: [32]). Try possible operations.\n    |- Try 28 + 21 = 49. Add 49 to the number set. Current number set: [49, 32], target: 39, just two numbers left.\n     |- Try 49 + 32 = 81. Evaluate 81 != 39, drop this branch.\n     |- Try 49 - 32 = 17. Evaluate 17 != 39, drop this branch.\n     |- Try 49 * 32 = 1568. Evaluate 1568 != 39, drop this branch.\n     |- Try 49 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 28 - 21 = 7. Add 7 to the number set. Current number set: [7, 32], target: 39, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 == 39, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 + 7 = 39\nThe step before: 28 - 21 = 7\nThe first step: 29 - 8 = 21\n\nOutput the solution in the required format:\n<Solution>\n29 - 8 = 21\n28 - 21 = 7\n32 + 7 = 39\n<\/Solution>\n","item":{"nums":[8,29,28,32],"solution":["29 - 8 = 21","28 - 21 = 7","32 + 7 = 39"],"target":39}}
+{"instance_id":"countdown_2k_189","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 9, 18, 47]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [6, 9, 18, 47], target: 26. Options for choosing two numbers: [(6, 9), (6, 18), (6, 47), (9, 18), (9, 47), (18, 47)].\n |- Pick two numbers (6, 9) (numbers left: [18, 47]). Try possible operations.\n  |- Try 9 + 6 = 15. Add 15 to the number set. Current number set: [15, 18, 47], target: 26. Options for choosing two numbers: [(15, 18), (15, 47), (18, 47)].\n   |- Pick two numbers (15, 18) (numbers left: [47]). Try possible operations.\n    |- Try 18 + 15 = 33. Add 33 to the number set. Current number set: [33, 47], target: 26, just two numbers left.\n     |- Try 47 + 33 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 47 - 33 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 47 * 33 = 1551. Evaluate 1551 != 26, drop this branch.\n     |- Try 47 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 18 - 15 = 3. Add 3 to the number set. Current number set: [3, 47], target: 26, just two numbers left.\n     |- Try 47 + 3 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 47 - 3 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 47 * 3 = 141. Evaluate 141 != 26, drop this branch.\n     |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n    |- Try 18 * 15 = 270. Add 270 to the number set. Current number set: [270, 47], target: 26, just two numbers left.\n     |- Try 270 + 47 = 317. Evaluate 317 != 26, drop this branch.\n     |- Try 270 - 47 = 223. Evaluate 223 != 26, drop this branch.\n     |- Try 270 * 47 = 12690. 12690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 47 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 18 \/ 15 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 47) (numbers left: [18]). Try possible operations.\n    |- Try 47 + 15 = 62. Add 62 to the number set. Current number set: [62, 18], target: 26, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 26, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 47 - 15 = 32. Add 32 to the number set. Current number set: [32, 18], target: 26, just two numbers left.\n     |- Try 32 + 18 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 32 - 18 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 32 * 18 = 576. Evaluate 576 != 26, drop this branch.\n     |- Try 32 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 47 * 15 = 705. Add 705 to the number set. Current number set: [705, 18], target: 26, just two numbers left.\n     |- Try 705 + 18 = 723. Evaluate 723 != 26, drop this branch.\n     |- Try 705 - 18 = 687. Evaluate 687 != 26, drop this branch.\n     |- Try 705 * 18 = 12690. 12690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 705 \/ 18 = 39.2. 39.2 is a decimal, drop this branch.\n    |- Try 47 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (18, 47) (numbers left: [15]). Try possible operations.\n    |- Try 47 + 18 = 65. Add 65 to the number set. Current number set: [65, 15], target: 26, just two numbers left.\n     |- Try 65 + 15 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 65 - 15 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 65 * 15 = 975. Evaluate 975 != 26, drop this branch.\n     |- Try 65 \/ 15 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 47 - 18 = 29. Add 29 to the number set. Current number set: [29, 15], target: 26, just two numbers left.\n     |- Try 29 + 15 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 29 - 15 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 29 * 15 = 435. Evaluate 435 != 26, drop this branch.\n     |- Try 29 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 47 * 18 = 846. Add 846 to the number set. Current number set: [846, 15], target: 26, just two numbers left.\n     |- Try 846 + 15 = 861. Evaluate 861 != 26, drop this branch.\n     |- Try 846 - 15 = 831. Evaluate 831 != 26, drop this branch.\n     |- Try 846 * 15 = 12690. 12690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 846 \/ 15 = 56.4. 56.4 is a decimal, drop this branch.\n    |- Try 47 \/ 18 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 9 - 6 = 3. Add 3 to the number set. Current number set: [3, 18, 47], target: 26. Options for choosing two numbers: [(3, 18), (3, 47), (18, 47)].\n   |- Pick two numbers (3, 18) (numbers left: [47]). Try possible operations.\n    |- Try 18 + 3 = 21. Add 21 to the number set. Current number set: [21, 47], target: 26, just two numbers left.\n     |- Try 47 + 21 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 47 - 21 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 - 21 = 26\nThe step before: 18 + 3 = 21\nThe first step: 9 - 6 = 3\n\nOutput the solution in the required format:\n<Solution>\n9 - 6 = 3\n18 + 3 = 21\n47 - 21 = 26\n<\/Solution>\n","item":{"nums":[6,9,18,47],"solution":["9 - 6 = 3","18 + 3 = 21","47 - 21 = 26"],"target":26}}
+{"instance_id":"countdown_2k_190","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 12, 3, 27]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [46, 12, 3, 27], target: 23. Options for choosing two numbers: [(46, 12), (46, 3), (46, 27), (12, 3), (12, 27), (3, 27)].\n |- Pick two numbers (46, 12) (numbers left: [3, 27]). Try possible operations.\n  |- Try 46 + 12 = 58. Add 58 to the number set. Current number set: [58, 3, 27], target: 23. Options for choosing two numbers: [(58, 3), (58, 27), (3, 27)].\n   |- Pick two numbers (58, 3) (numbers left: [27]). Try possible operations.\n    |- Try 58 + 3 = 61. Add 61 to the number set. Current number set: [61, 27], target: 23, just two numbers left.\n     |- Try 61 + 27 = 88. Evaluate 88 != 23, drop this branch.\n     |- Try 61 - 27 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 61 * 27 = 1647. Evaluate 1647 != 23, drop this branch.\n     |- Try 61 \/ 27 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 58 - 3 = 55. Add 55 to the number set. Current number set: [55, 27], target: 23, just two numbers left.\n     |- Try 55 + 27 = 82. Evaluate 82 != 23, drop this branch.\n     |- Try 55 - 27 = 28. Evaluate 28 != 23, drop this branch.\n     |- Try 55 * 27 = 1485. Evaluate 1485 != 23, drop this branch.\n     |- Try 55 \/ 27 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 58 * 3 = 174. Add 174 to the number set. Current number set: [174, 27], target: 23, just two numbers left.\n     |- Try 174 + 27 = 201. Evaluate 201 != 23, drop this branch.\n     |- Try 174 - 27 = 147. Evaluate 147 != 23, drop this branch.\n     |- Try 174 * 27 = 4698. 4698 exceeds the maximum intermediate result, drop this branch.\n     |- Try 174 \/ 27 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 58 \/ 3 = 19.3. 19.3 is a decimal, drop this branch.\n   |- Pick two numbers (58, 27) (numbers left: [3]). Try possible operations.\n    |- Try 58 + 27 = 85. Add 85 to the number set. Current number set: [85, 3], target: 23, just two numbers left.\n     |- Try 85 + 3 = 88. Evaluate 88 != 23, drop this branch.\n     |- Try 85 - 3 = 82. Evaluate 82 != 23, drop this branch.\n     |- Try 85 * 3 = 255. Evaluate 255 != 23, drop this branch.\n     |- Try 85 \/ 3 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 58 - 27 = 31. Add 31 to the number set. Current number set: [31, 3], target: 23, just two numbers left.\n     |- Try 31 + 3 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 31 - 3 = 28. Evaluate 28 != 23, drop this branch.\n     |- Try 31 * 3 = 93. Evaluate 93 != 23, drop this branch.\n     |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 58 * 27 = 1566. Add 1566 to the number set. Current number set: [1566, 3], target: 23, just two numbers left.\n     |- Try 1566 + 3 = 1569. Evaluate 1569 != 23, drop this branch.\n     |- Try 1566 - 3 = 1563. Evaluate 1563 != 23, drop this branch.\n     |- Try 1566 * 3 = 4698. 4698 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1566 \/ 3 = 522. Evaluate 522 != 23, drop this branch.\n    |- Try 58 \/ 27 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (3, 27) (numbers left: [58]). Try possible operations.\n    |- Try 27 + 3 = 30. Add 30 to the number set. Current number set: [30, 58], target: 23, just two numbers left.\n     |- Try 58 + 30 = 88. Evaluate 88 != 23, drop this branch.\n     |- Try 58 - 30 = 28. Evaluate 28 != 23, drop this branch.\n     |- Try 58 * 30 = 1740. Evaluate 1740 != 23, drop this branch.\n     |- Try 58 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 27 - 3 = 24. Add 24 to the number set. Current number set: [24, 58], target: 23, just two numbers left.\n     |- Try 58 + 24 = 82. Evaluate 82 != 23, drop this branch.\n     |- Try 58 - 24 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 58 * 24 = 1392. Evaluate 1392 != 23, drop this branch.\n     |- Try 58 \/ 24 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 27 * 3 = 81. Add 81 to the number set. Current number set: [81, 58], target: 23, just two numbers left.\n     |- Try 81 + 58 = 139. Evaluate 139 != 23, drop this branch.\n     |- Try 81 - 58 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 81 - 58 = 23\nThe step before: 27 * 3 = 81\nThe first step: 46 + 12 = 58\n\nOutput the solution in the required format:\n<Solution>\n46 + 12 = 58\n27 * 3 = 81\n81 - 58 = 23\n<\/Solution>\n","item":{"nums":[46,12,3,27],"solution":["46 + 12 = 58","27 * 3 = 81","81 - 58 = 23"],"target":23}}
+{"instance_id":"countdown_2k_191","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 18, 48, 8]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [3, 18, 48, 8], target: 25. Options for choosing two numbers: [(3, 18), (3, 48), (3, 8), (18, 48), (18, 8), (48, 8)].\n |- Pick two numbers (3, 18) (numbers left: [48, 8]). Try possible operations.\n  |- Try 18 + 3 = 21. Add 21 to the number set. Current number set: [21, 48, 8], target: 25. Options for choosing two numbers: [(21, 48), (21, 8), (48, 8)].\n   |- Pick two numbers (21, 48) (numbers left: [8]). Try possible operations.\n    |- Try 48 + 21 = 69. Add 69 to the number set. Current number set: [69, 8], target: 25, just two numbers left.\n     |- Try 69 + 8 = 77. Evaluate 77 != 25, drop this branch.\n     |- Try 69 - 8 = 61. Evaluate 61 != 25, drop this branch.\n     |- Try 69 * 8 = 552. Evaluate 552 != 25, drop this branch.\n     |- Try 69 \/ 8 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 48 - 21 = 27. Add 27 to the number set. Current number set: [27, 8], target: 25, just two numbers left.\n     |- Try 27 + 8 = 35. Evaluate 35 != 25, drop this branch.\n     |- Try 27 - 8 = 19. Evaluate 19 != 25, drop this branch.\n     |- Try 27 * 8 = 216. Evaluate 216 != 25, drop this branch.\n     |- Try 27 \/ 8 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 48 * 21 = 1008. Add 1008 to the number set. Current number set: [1008, 8], target: 25, just two numbers left.\n     |- Try 1008 + 8 = 1016. Evaluate 1016 != 25, drop this branch.\n     |- Try 1008 - 8 = 1000. Evaluate 1000 != 25, drop this branch.\n     |- Try 1008 * 8 = 8064. 8064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 8 = 126. Evaluate 126 != 25, drop this branch.\n    |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (21, 8) (numbers left: [48]). Try possible operations.\n    |- Try 21 + 8 = 29. Add 29 to the number set. Current number set: [29, 48], target: 25, just two numbers left.\n     |- Try 48 + 29 = 77. Evaluate 77 != 25, drop this branch.\n     |- Try 48 - 29 = 19. Evaluate 19 != 25, drop this branch.\n     |- Try 48 * 29 = 1392. Evaluate 1392 != 25, drop this branch.\n     |- Try 48 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 - 8 = 13. Add 13 to the number set. Current number set: [13, 48], target: 25, just two numbers left.\n     |- Try 48 + 13 = 61. Evaluate 61 != 25, drop this branch.\n     |- Try 48 - 13 = 35. Evaluate 35 != 25, drop this branch.\n     |- Try 48 * 13 = 624. Evaluate 624 != 25, drop this branch.\n     |- Try 48 \/ 13 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 21 * 8 = 168. Add 168 to the number set. Current number set: [168, 48], target: 25, just two numbers left.\n     |- Try 168 + 48 = 216. Evaluate 216 != 25, drop this branch.\n     |- Try 168 - 48 = 120. Evaluate 120 != 25, drop this branch.\n     |- Try 168 * 48 = 8064. 8064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 48 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (48, 8) (numbers left: [21]). Try possible operations.\n    |- Try 48 + 8 = 56. Add 56 to the number set. Current number set: [56, 21], target: 25, just two numbers left.\n     |- Try 56 + 21 = 77. Evaluate 77 != 25, drop this branch.\n     |- Try 56 - 21 = 35. Evaluate 35 != 25, drop this branch.\n     |- Try 56 * 21 = 1176. Evaluate 1176 != 25, drop this branch.\n     |- Try 56 \/ 21 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 48 - 8 = 40. Add 40 to the number set. Current number set: [40, 21], target: 25, just two numbers left.\n     |- Try 40 + 21 = 61. Evaluate 61 != 25, drop this branch.\n     |- Try 40 - 21 = 19. Evaluate 19 != 25, drop this branch.\n     |- Try 40 * 21 = 840. Evaluate 840 != 25, drop this branch.\n     |- Try 40 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 48 * 8 = 384. Add 384 to the number set. Current number set: [384, 21], target: 25, just two numbers left.\n     |- Try 384 + 21 = 405. Evaluate 405 != 25, drop this branch.\n     |- Try 384 - 21 = 363. Evaluate 363 != 25, drop this branch.\n     |- Try 384 * 21 = 8064. 8064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 384 \/ 21 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 48 \/ 8 = 6. Add 6 to the number set. Current number set: [6, 21], target: 25, just two numbers left.\n     |- Try 21 + 6 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 21 - 6 = 15. Evaluate 15 != 25, drop this branch.\n     |- Try 21 * 6 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 21 \/ 6 = 3.5. 3.5 is a decimal, drop this branch.\n  |- Try 18 - 3 = 15. Add 15 to the number set. Current number set: [15, 48, 8], target: 25. Options for choosing two numbers: [(15, 48), (15, 8), (48, 8)].\n   |- Pick two numbers (15, 48) (numbers left: [8]). Try possible operations.\n    |- Try 48 + 15 = 63. Add 63 to the number set. Current number set: [63, 8], target: 25, just two numbers left.\n     |- Try 63 + 8 = 71. Evaluate 71 != 25, drop this branch.\n     |- Try 63 - 8 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 63 * 8 = 504. Evaluate 504 != 25, drop this branch.\n     |- Try 63 \/ 8 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 48 - 15 = 33. Add 33 to the number set. Current number set: [33, 8], target: 25, just two numbers left.\n     |- Try 33 + 8 = 41. Evaluate 41 != 25, drop this branch.\n     |- Try 33 - 8 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 - 8 = 25\nThe step before: 48 - 15 = 33\nThe first step: 18 - 3 = 15\n\nOutput the solution in the required format:\n<Solution>\n18 - 3 = 15\n48 - 15 = 33\n33 - 8 = 25\n<\/Solution>\n","item":{"nums":[3,18,48,8],"solution":["18 - 3 = 15","48 - 15 = 33","33 - 8 = 25"],"target":25}}
+{"instance_id":"countdown_2k_192","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 16, 25, 2]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [33, 16, 25, 2], target: 44. Options for choosing two numbers: [(33, 16), (33, 25), (33, 2), (16, 25), (16, 2), (25, 2)].\n |- Pick two numbers (33, 16) (numbers left: [25, 2]). Try possible operations.\n  |- Try 33 + 16 = 49. Add 49 to the number set. Current number set: [49, 25, 2], target: 44. Options for choosing two numbers: [(49, 25), (49, 2), (25, 2)].\n   |- Pick two numbers (49, 25) (numbers left: [2]). Try possible operations.\n    |- Try 49 + 25 = 74. Add 74 to the number set. Current number set: [74, 2], target: 44, just two numbers left.\n     |- Try 74 + 2 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 74 - 2 = 72. Evaluate 72 != 44, drop this branch.\n     |- Try 74 * 2 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 74 \/ 2 = 37. Evaluate 37 != 44, drop this branch.\n    |- Try 49 - 25 = 24. Add 24 to the number set. Current number set: [24, 2], target: 44, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 44, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 44, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 44, drop this branch.\n    |- Try 49 * 25 = 1225. Add 1225 to the number set. Current number set: [1225, 2], target: 44, just two numbers left.\n     |- Try 1225 + 2 = 1227. Evaluate 1227 != 44, drop this branch.\n     |- Try 1225 - 2 = 1223. Evaluate 1223 != 44, drop this branch.\n     |- Try 1225 * 2 = 2450. 2450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1225 \/ 2 = 612.5. 612.5 is a decimal, drop this branch.\n    |- Try 49 \/ 25 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (49, 2) (numbers left: [25]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 25], target: 44, just two numbers left.\n     |- Try 51 + 25 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 51 - 25 = 26. Evaluate 26 != 44, drop this branch.\n     |- Try 51 * 25 = 1275. Evaluate 1275 != 44, drop this branch.\n     |- Try 51 \/ 25 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 25], target: 44, just two numbers left.\n     |- Try 47 + 25 = 72. Evaluate 72 != 44, drop this branch.\n     |- Try 47 - 25 = 22. Evaluate 22 != 44, drop this branch.\n     |- Try 47 * 25 = 1175. Evaluate 1175 != 44, drop this branch.\n     |- Try 47 \/ 25 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 25], target: 44, just two numbers left.\n     |- Try 98 + 25 = 123. Evaluate 123 != 44, drop this branch.\n     |- Try 98 - 25 = 73. Evaluate 73 != 44, drop this branch.\n     |- Try 98 * 25 = 2450. 2450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 25 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n   |- Pick two numbers (25, 2) (numbers left: [49]). Try possible operations.\n    |- Try 25 + 2 = 27. Add 27 to the number set. Current number set: [27, 49], target: 44, just two numbers left.\n     |- Try 49 + 27 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 49 - 27 = 22. Evaluate 22 != 44, drop this branch.\n     |- Try 49 * 27 = 1323. Evaluate 1323 != 44, drop this branch.\n     |- Try 49 \/ 27 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 25 - 2 = 23. Add 23 to the number set. Current number set: [23, 49], target: 44, just two numbers left.\n     |- Try 49 + 23 = 72. Evaluate 72 != 44, drop this branch.\n     |- Try 49 - 23 = 26. Evaluate 26 != 44, drop this branch.\n     |- Try 49 * 23 = 1127. Evaluate 1127 != 44, drop this branch.\n     |- Try 49 \/ 23 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 25 * 2 = 50. Add 50 to the number set. Current number set: [50, 49], target: 44, just two numbers left.\n     |- Try 50 + 49 = 99. Evaluate 99 != 44, drop this branch.\n     |- Try 50 - 49 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 50 * 49 = 2450. 2450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 49 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n  |- Try 33 - 16 = 17. Add 17 to the number set. Current number set: [17, 25, 2], target: 44. Options for choosing two numbers: [(17, 25), (17, 2), (25, 2)].\n   |- Pick two numbers (17, 25) (numbers left: [2]). Try possible operations.\n    |- Try 25 + 17 = 42. Add 42 to the number set. Current number set: [42, 2], target: 44, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 42 + 2 = 44\nThe step before: 25 + 17 = 42\nThe first step: 33 - 16 = 17\n\nOutput the solution in the required format:\n<Solution>\n33 - 16 = 17\n25 + 17 = 42\n42 + 2 = 44\n<\/Solution>\n","item":{"nums":[33,16,25,2],"solution":["33 - 16 = 17","25 + 17 = 42","42 + 2 = 44"],"target":44}}
+{"instance_id":"countdown_2k_193","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 3, 28, 32]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [8, 3, 28, 32], target: 44. Options for choosing two numbers: [(8, 3), (8, 28), (8, 32), (3, 28), (3, 32), (28, 32)].\n |- Pick two numbers (8, 3) (numbers left: [28, 32]). Try possible operations.\n  |- Try 8 + 3 = 11. Add 11 to the number set. Current number set: [11, 28, 32], target: 44. Options for choosing two numbers: [(11, 28), (11, 32), (28, 32)].\n   |- Pick two numbers (11, 28) (numbers left: [32]). Try possible operations.\n    |- Try 28 + 11 = 39. Add 39 to the number set. Current number set: [39, 32], target: 44, just two numbers left.\n     |- Try 39 + 32 = 71. Evaluate 71 != 44, drop this branch.\n     |- Try 39 - 32 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 39 * 32 = 1248. Evaluate 1248 != 44, drop this branch.\n     |- Try 39 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 11 = 17. Add 17 to the number set. Current number set: [17, 32], target: 44, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 44, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 28 * 11 = 308. Add 308 to the number set. Current number set: [308, 32], target: 44, just two numbers left.\n     |- Try 308 + 32 = 340. Evaluate 340 != 44, drop this branch.\n     |- Try 308 - 32 = 276. Evaluate 276 != 44, drop this branch.\n     |- Try 308 * 32 = 9856. 9856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 308 \/ 32 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 28 \/ 11 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (11, 32) (numbers left: [28]). Try possible operations.\n    |- Try 32 + 11 = 43. Add 43 to the number set. Current number set: [43, 28], target: 44, just two numbers left.\n     |- Try 43 + 28 = 71. Evaluate 71 != 44, drop this branch.\n     |- Try 43 - 28 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 43 * 28 = 1204. Evaluate 1204 != 44, drop this branch.\n     |- Try 43 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 32 - 11 = 21. Add 21 to the number set. Current number set: [21, 28], target: 44, just two numbers left.\n     |- Try 28 + 21 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 28 - 21 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 28 * 21 = 588. Evaluate 588 != 44, drop this branch.\n     |- Try 28 \/ 21 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 32 * 11 = 352. Add 352 to the number set. Current number set: [352, 28], target: 44, just two numbers left.\n     |- Try 352 + 28 = 380. Evaluate 380 != 44, drop this branch.\n     |- Try 352 - 28 = 324. Evaluate 324 != 44, drop this branch.\n     |- Try 352 * 28 = 9856. 9856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 28 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (28, 32) (numbers left: [11]). Try possible operations.\n    |- Try 32 + 28 = 60. Add 60 to the number set. Current number set: [60, 11], target: 44, just two numbers left.\n     |- Try 60 + 11 = 71. Evaluate 71 != 44, drop this branch.\n     |- Try 60 - 11 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 60 * 11 = 660. Evaluate 660 != 44, drop this branch.\n     |- Try 60 \/ 11 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 32 - 28 = 4. Add 4 to the number set. Current number set: [4, 11], target: 44, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 11 * 4 = 44\nThe step before: 32 - 28 = 4\nThe first step: 8 + 3 = 11\n\nOutput the solution in the required format:\n<Solution>\n8 + 3 = 11\n32 - 28 = 4\n11 * 4 = 44\n<\/Solution>\n","item":{"nums":[8,3,28,32],"solution":["8 + 3 = 11","32 - 28 = 4","11 * 4 = 44"],"target":44}}
+{"instance_id":"countdown_2k_194","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 42, 43, 13]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [35, 42, 43, 13], target: 37. Options for choosing two numbers: [(35, 42), (35, 43), (35, 13), (42, 43), (42, 13), (43, 13)].\n |- Pick two numbers (35, 42) (numbers left: [43, 13]). Try possible operations.\n  |- Try 42 + 35 = 77. Add 77 to the number set. Current number set: [77, 43, 13], target: 37. Options for choosing two numbers: [(77, 43), (77, 13), (43, 13)].\n   |- Pick two numbers (77, 43) (numbers left: [13]). Try possible operations.\n    |- Try 77 + 43 = 120. Add 120 to the number set. Current number set: [120, 13], target: 37, just two numbers left.\n     |- Try 120 + 13 = 133. Evaluate 133 != 37, drop this branch.\n     |- Try 120 - 13 = 107. Evaluate 107 != 37, drop this branch.\n     |- Try 120 * 13 = 1560. Evaluate 1560 != 37, drop this branch.\n     |- Try 120 \/ 13 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 77 - 43 = 34. Add 34 to the number set. Current number set: [34, 13], target: 37, just two numbers left.\n     |- Try 34 + 13 = 47. Evaluate 47 != 37, drop this branch.\n     |- Try 34 - 13 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 34 * 13 = 442. Evaluate 442 != 37, drop this branch.\n     |- Try 34 \/ 13 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 77 * 43 = 3311. 3311 exceeds the maximum intermediate result, drop this branch.\n    |- Try 77 \/ 43 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (77, 13) (numbers left: [43]). Try possible operations.\n    |- Try 77 + 13 = 90. Add 90 to the number set. Current number set: [90, 43], target: 37, just two numbers left.\n     |- Try 90 + 43 = 133. Evaluate 133 != 37, drop this branch.\n     |- Try 90 - 43 = 47. Evaluate 47 != 37, drop this branch.\n     |- Try 90 * 43 = 3870. 3870 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 43 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 77 - 13 = 64. Add 64 to the number set. Current number set: [64, 43], target: 37, just two numbers left.\n     |- Try 64 + 43 = 107. Evaluate 107 != 37, drop this branch.\n     |- Try 64 - 43 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 64 * 43 = 2752. 2752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 43 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 77 * 13 = 1001. Add 1001 to the number set. Current number set: [1001, 43], target: 37, just two numbers left.\n     |- Try 1001 + 43 = 1044. Evaluate 1044 != 37, drop this branch.\n     |- Try 1001 - 43 = 958. Evaluate 958 != 37, drop this branch.\n     |- Try 1001 * 43 = 43043. 43043 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1001 \/ 43 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 77 \/ 13 = 5.9. 5.9 is a decimal, drop this branch.\n   |- Pick two numbers (43, 13) (numbers left: [77]). Try possible operations.\n    |- Try 43 + 13 = 56. Add 56 to the number set. Current number set: [56, 77], target: 37, just two numbers left.\n     |- Try 77 + 56 = 133. Evaluate 133 != 37, drop this branch.\n     |- Try 77 - 56 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 77 * 56 = 4312. 4312 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 56 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 43 - 13 = 30. Add 30 to the number set. Current number set: [30, 77], target: 37, just two numbers left.\n     |- Try 77 + 30 = 107. Evaluate 107 != 37, drop this branch.\n     |- Try 77 - 30 = 47. Evaluate 47 != 37, drop this branch.\n     |- Try 77 * 30 = 2310. 2310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 43 * 13 = 559. Add 559 to the number set. Current number set: [559, 77], target: 37, just two numbers left.\n     |- Try 559 + 77 = 636. Evaluate 636 != 37, drop this branch.\n     |- Try 559 - 77 = 482. Evaluate 482 != 37, drop this branch.\n     |- Try 559 * 77 = 43043. 43043 exceeds the maximum intermediate result, drop this branch.\n     |- Try 559 \/ 77 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 43 \/ 13 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 42 - 35 = 7. Add 7 to the number set. Current number set: [7, 43, 13], target: 37. Options for choosing two numbers: [(7, 43), (7, 13), (43, 13)].\n   |- Pick two numbers (7, 43) (numbers left: [13]). Try possible operations.\n    |- Try 43 + 7 = 50. Add 50 to the number set. Current number set: [50, 13], target: 37, just two numbers left.\n     |- Try 50 + 13 = 63. Evaluate 63 != 37, drop this branch.\n     |- Try 50 - 13 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 50 - 13 = 37\nThe step before: 43 + 7 = 50\nThe first step: 42 - 35 = 7\n\nOutput the solution in the required format:\n<Solution>\n42 - 35 = 7\n43 + 7 = 50\n50 - 13 = 37\n<\/Solution>\n","item":{"nums":[35,42,43,13],"solution":["42 - 35 = 7","43 + 7 = 50","50 - 13 = 37"],"target":37}}
+{"instance_id":"countdown_2k_195","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 3, 45, 46]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [26, 3, 45, 46], target: 22. Options for choosing two numbers: [(26, 3), (26, 45), (26, 46), (3, 45), (3, 46), (45, 46)].\n |- Pick two numbers (26, 3) (numbers left: [45, 46]). Try possible operations.\n  |- Try 26 + 3 = 29. Add 29 to the number set. Current number set: [29, 45, 46], target: 22. Options for choosing two numbers: [(29, 45), (29, 46), (45, 46)].\n   |- Pick two numbers (29, 45) (numbers left: [46]). Try possible operations.\n    |- Try 45 + 29 = 74. Add 74 to the number set. Current number set: [74, 46], target: 22, just two numbers left.\n     |- Try 74 + 46 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 74 - 46 = 28. Evaluate 28 != 22, drop this branch.\n     |- Try 74 * 46 = 3404. 3404 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 46 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 45 - 29 = 16. Add 16 to the number set. Current number set: [16, 46], target: 22, just two numbers left.\n     |- Try 46 + 16 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 46 - 16 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 46 * 16 = 736. Evaluate 736 != 22, drop this branch.\n     |- Try 46 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 45 * 29 = 1305. Add 1305 to the number set. Current number set: [1305, 46], target: 22, just two numbers left.\n     |- Try 1305 + 46 = 1351. Evaluate 1351 != 22, drop this branch.\n     |- Try 1305 - 46 = 1259. Evaluate 1259 != 22, drop this branch.\n     |- Try 1305 * 46 = 60030. 60030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1305 \/ 46 = 28.4. 28.4 is a decimal, drop this branch.\n    |- Try 45 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (29, 46) (numbers left: [45]). Try possible operations.\n    |- Try 46 + 29 = 75. Add 75 to the number set. Current number set: [75, 45], target: 22, just two numbers left.\n     |- Try 75 + 45 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 75 - 45 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 75 * 45 = 3375. 3375 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 45 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 46 - 29 = 17. Add 17 to the number set. Current number set: [17, 45], target: 22, just two numbers left.\n     |- Try 45 + 17 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 45 - 17 = 28. Evaluate 28 != 22, drop this branch.\n     |- Try 45 * 17 = 765. Evaluate 765 != 22, drop this branch.\n     |- Try 45 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 46 * 29 = 1334. Add 1334 to the number set. Current number set: [1334, 45], target: 22, just two numbers left.\n     |- Try 1334 + 45 = 1379. Evaluate 1379 != 22, drop this branch.\n     |- Try 1334 - 45 = 1289. Evaluate 1289 != 22, drop this branch.\n     |- Try 1334 * 45 = 60030. 60030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 45 = 29.6. 29.6 is a decimal, drop this branch.\n    |- Try 46 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (45, 46) (numbers left: [29]). Try possible operations.\n    |- Try 46 + 45 = 91. Add 91 to the number set. Current number set: [91, 29], target: 22, just two numbers left.\n     |- Try 91 + 29 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 91 - 29 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 91 * 29 = 2639. 2639 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 29 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 46 - 45 = 1. Add 1 to the number set. Current number set: [1, 29], target: 22, just two numbers left.\n     |- Try 29 + 1 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 29 - 1 = 28. Evaluate 28 != 22, drop this branch.\n     |- Try 29 * 1 = 29. Evaluate 29 != 22, drop this branch.\n     |- Try 29 \/ 1 = 29. Evaluate 29 != 22, drop this branch.\n    |- Try 46 * 45 = 2070. 2070 exceeds the maximum intermediate result, drop this branch.\n    |- Try 46 \/ 45 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 26 - 3 = 23. Add 23 to the number set. Current number set: [23, 45, 46], target: 22. Options for choosing two numbers: [(23, 45), (23, 46), (45, 46)].\n   |- Pick two numbers (23, 45) (numbers left: [46]). Try possible operations.\n    |- Try 45 + 23 = 68. Add 68 to the number set. Current number set: [68, 46], target: 22, just two numbers left.\n     |- Try 68 + 46 = 114. Evaluate 114 != 22, drop this branch.\n     |- Try 68 - 46 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 68 - 46 = 22\nThe step before: 45 + 23 = 68\nThe first step: 26 - 3 = 23\n\nOutput the solution in the required format:\n<Solution>\n26 - 3 = 23\n45 + 23 = 68\n68 - 46 = 22\n<\/Solution>\n","item":{"nums":[26,3,45,46],"solution":["26 - 3 = 23","45 + 23 = 68","68 - 46 = 22"],"target":22}}
+{"instance_id":"countdown_2k_196","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 6, 8, 6]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [30, 6, 8, 6], target: 27. Options for choosing two numbers: [(30, 6), (30, 8), (30, 6), (6, 8), (6, 6), (8, 6)].\n |- Pick two numbers (30, 6) (numbers left: [8, 6]). Try possible operations.\n  |- Try 30 + 6 = 36. Add 36 to the number set. Current number set: [36, 8, 6], target: 27. Options for choosing two numbers: [(36, 8), (36, 6), (8, 6)].\n   |- Pick two numbers (36, 8) (numbers left: [6]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 6], target: 27, just two numbers left.\n     |- Try 44 + 6 = 50. Evaluate 50 != 27, drop this branch.\n     |- Try 44 - 6 = 38. Evaluate 38 != 27, drop this branch.\n     |- Try 44 * 6 = 264. Evaluate 264 != 27, drop this branch.\n     |- Try 44 \/ 6 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 6], target: 27, just two numbers left.\n     |- Try 28 + 6 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 28 - 6 = 22. Evaluate 22 != 27, drop this branch.\n     |- Try 28 * 6 = 168. Evaluate 168 != 27, drop this branch.\n     |- Try 28 \/ 6 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 6], target: 27, just two numbers left.\n     |- Try 288 + 6 = 294. Evaluate 294 != 27, drop this branch.\n     |- Try 288 - 6 = 282. Evaluate 282 != 27, drop this branch.\n     |- Try 288 * 6 = 1728. Evaluate 1728 != 27, drop this branch.\n     |- Try 288 \/ 6 = 48. Evaluate 48 != 27, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (36, 6) (numbers left: [8]). Try possible operations.\n    |- Try 36 + 6 = 42. Add 42 to the number set. Current number set: [42, 8], target: 27, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 27, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 27, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 36 - 6 = 30. Add 30 to the number set. Current number set: [30, 8], target: 27, just two numbers left.\n     |- Try 30 + 8 = 38. Evaluate 38 != 27, drop this branch.\n     |- Try 30 - 8 = 22. Evaluate 22 != 27, drop this branch.\n     |- Try 30 * 8 = 240. Evaluate 240 != 27, drop this branch.\n     |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 36 * 6 = 216. Add 216 to the number set. Current number set: [216, 8], target: 27, just two numbers left.\n     |- Try 216 + 8 = 224. Evaluate 224 != 27, drop this branch.\n     |- Try 216 - 8 = 208. Evaluate 208 != 27, drop this branch.\n     |- Try 216 * 8 = 1728. Evaluate 1728 != 27, drop this branch.\n     |- Try 216 \/ 8 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 216 \/ 8 = 27\nThe step before: 36 * 6 = 216\nThe first step: 30 + 6 = 36\n\nOutput the solution in the required format:\n<Solution>\n30 + 6 = 36\n36 * 6 = 216\n216 \/ 8 = 27\n<\/Solution>\n","item":{"nums":[30,6,8,6],"solution":["30 + 6 = 36","36 * 6 = 216","216 \/ 8 = 27"],"target":27}}
+{"instance_id":"countdown_2k_197","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 45, 33, 36]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [22, 45, 33, 36], target: 46. Options for choosing two numbers: [(22, 45), (22, 33), (22, 36), (45, 33), (45, 36), (33, 36)].\n |- Pick two numbers (22, 45) (numbers left: [33, 36]). Try possible operations.\n  |- Try 45 + 22 = 67. Add 67 to the number set. Current number set: [67, 33, 36], target: 46. Options for choosing two numbers: [(67, 33), (67, 36), (33, 36)].\n   |- Pick two numbers (67, 33) (numbers left: [36]). Try possible operations.\n    |- Try 67 + 33 = 100. Add 100 to the number set. Current number set: [100, 36], target: 46, just two numbers left.\n     |- Try 100 + 36 = 136. Evaluate 136 != 46, drop this branch.\n     |- Try 100 - 36 = 64. Evaluate 64 != 46, drop this branch.\n     |- Try 100 * 36 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 36 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 67 - 33 = 34. Add 34 to the number set. Current number set: [34, 36], target: 46, just two numbers left.\n     |- Try 36 + 34 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 36 - 34 = 2. Evaluate 2 != 46, drop this branch.\n     |- Try 36 * 34 = 1224. Evaluate 1224 != 46, drop this branch.\n     |- Try 36 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 67 * 33 = 2211. 2211 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 33 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (67, 36) (numbers left: [33]). Try possible operations.\n    |- Try 67 + 36 = 103. Add 103 to the number set. Current number set: [103, 33], target: 46, just two numbers left.\n     |- Try 103 + 33 = 136. Evaluate 136 != 46, drop this branch.\n     |- Try 103 - 33 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 103 * 33 = 3399. 3399 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 33 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 67 - 36 = 31. Add 31 to the number set. Current number set: [31, 33], target: 46, just two numbers left.\n     |- Try 33 + 31 = 64. Evaluate 64 != 46, drop this branch.\n     |- Try 33 - 31 = 2. Evaluate 2 != 46, drop this branch.\n     |- Try 33 * 31 = 1023. Evaluate 1023 != 46, drop this branch.\n     |- Try 33 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 67 * 36 = 2412. 2412 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 36 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (33, 36) (numbers left: [67]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 67], target: 46, just two numbers left.\n     |- Try 69 + 67 = 136. Evaluate 136 != 46, drop this branch.\n     |- Try 69 - 67 = 2. Evaluate 2 != 46, drop this branch.\n     |- Try 69 * 67 = 4623. 4623 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 67 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 33 = 3. Add 3 to the number set. Current number set: [3, 67], target: 46, just two numbers left.\n     |- Try 67 + 3 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 67 - 3 = 64. Evaluate 64 != 46, drop this branch.\n     |- Try 67 * 3 = 201. Evaluate 201 != 46, drop this branch.\n     |- Try 67 \/ 3 = 22.3. 22.3 is a decimal, drop this branch.\n    |- Try 36 * 33 = 1188. Add 1188 to the number set. Current number set: [1188, 67], target: 46, just two numbers left.\n     |- Try 1188 + 67 = 1255. Evaluate 1255 != 46, drop this branch.\n     |- Try 1188 - 67 = 1121. Evaluate 1121 != 46, drop this branch.\n     |- Try 1188 * 67 = 79596. 79596 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 67 = 17.7. 17.7 is a decimal, drop this branch.\n    |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 45 - 22 = 23. Add 23 to the number set. Current number set: [23, 33, 36], target: 46. Options for choosing two numbers: [(23, 33), (23, 36), (33, 36)].\n   |- Pick two numbers (23, 33) (numbers left: [36]). Try possible operations.\n    |- Try 33 + 23 = 56. Add 56 to the number set. Current number set: [56, 36], target: 46, just two numbers left.\n     |- Try 56 + 36 = 92. Evaluate 92 != 46, drop this branch.\n     |- Try 56 - 36 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 56 * 36 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 36 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 33 - 23 = 10. Add 10 to the number set. Current number set: [10, 36], target: 46, just two numbers left.\n     |- Try 36 + 10 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 + 10 = 46\nThe step before: 33 - 23 = 10\nThe first step: 45 - 22 = 23\n\nOutput the solution in the required format:\n<Solution>\n45 - 22 = 23\n33 - 23 = 10\n36 + 10 = 46\n<\/Solution>\n","item":{"nums":[22,45,33,36],"solution":["45 - 22 = 23","33 - 23 = 10","36 + 10 = 46"],"target":46}}
+{"instance_id":"countdown_2k_198","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 45, 28, 47]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [37, 45, 28, 47], target: 11. Options for choosing two numbers: [(37, 45), (37, 28), (37, 47), (45, 28), (45, 47), (28, 47)].\n |- Pick two numbers (37, 45) (numbers left: [28, 47]). Try possible operations.\n  |- Try 45 + 37 = 82. Add 82 to the number set. Current number set: [82, 28, 47], target: 11. Options for choosing two numbers: [(82, 28), (82, 47), (28, 47)].\n   |- Pick two numbers (82, 28) (numbers left: [47]). Try possible operations.\n    |- Try 82 + 28 = 110. Add 110 to the number set. Current number set: [110, 47], target: 11, just two numbers left.\n     |- Try 110 + 47 = 157. Evaluate 157 != 11, drop this branch.\n     |- Try 110 - 47 = 63. Evaluate 63 != 11, drop this branch.\n     |- Try 110 * 47 = 5170. 5170 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 47 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 82 - 28 = 54. Add 54 to the number set. Current number set: [54, 47], target: 11, just two numbers left.\n     |- Try 54 + 47 = 101. Evaluate 101 != 11, drop this branch.\n     |- Try 54 - 47 = 7. Evaluate 7 != 11, drop this branch.\n     |- Try 54 * 47 = 2538. 2538 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 82 * 28 = 2296. 2296 exceeds the maximum intermediate result, drop this branch.\n    |- Try 82 \/ 28 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (82, 47) (numbers left: [28]). Try possible operations.\n    |- Try 82 + 47 = 129. Add 129 to the number set. Current number set: [129, 28], target: 11, just two numbers left.\n     |- Try 129 + 28 = 157. Evaluate 157 != 11, drop this branch.\n     |- Try 129 - 28 = 101. Evaluate 101 != 11, drop this branch.\n     |- Try 129 * 28 = 3612. 3612 exceeds the maximum intermediate result, drop this branch.\n     |- Try 129 \/ 28 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 82 - 47 = 35. Add 35 to the number set. Current number set: [35, 28], target: 11, just two numbers left.\n     |- Try 35 + 28 = 63. Evaluate 63 != 11, drop this branch.\n     |- Try 35 - 28 = 7. Evaluate 7 != 11, drop this branch.\n     |- Try 35 * 28 = 980. Evaluate 980 != 11, drop this branch.\n     |- Try 35 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 82 * 47 = 3854. 3854 exceeds the maximum intermediate result, drop this branch.\n    |- Try 82 \/ 47 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (28, 47) (numbers left: [82]). Try possible operations.\n    |- Try 47 + 28 = 75. Add 75 to the number set. Current number set: [75, 82], target: 11, just two numbers left.\n     |- Try 82 + 75 = 157. Evaluate 157 != 11, drop this branch.\n     |- Try 82 - 75 = 7. Evaluate 7 != 11, drop this branch.\n     |- Try 82 * 75 = 6150. 6150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 75 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 47 - 28 = 19. Add 19 to the number set. Current number set: [19, 82], target: 11, just two numbers left.\n     |- Try 82 + 19 = 101. Evaluate 101 != 11, drop this branch.\n     |- Try 82 - 19 = 63. Evaluate 63 != 11, drop this branch.\n     |- Try 82 * 19 = 1558. Evaluate 1558 != 11, drop this branch.\n     |- Try 82 \/ 19 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 47 * 28 = 1316. Add 1316 to the number set. Current number set: [1316, 82], target: 11, just two numbers left.\n     |- Try 1316 + 82 = 1398. Evaluate 1398 != 11, drop this branch.\n     |- Try 1316 - 82 = 1234. Evaluate 1234 != 11, drop this branch.\n     |- Try 1316 * 82 = 107912. 107912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1316 \/ 82 = 16.0. 16.0 is a decimal, drop this branch.\n    |- Try 47 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 45 - 37 = 8. Add 8 to the number set. Current number set: [8, 28, 47], target: 11. Options for choosing two numbers: [(8, 28), (8, 47), (28, 47)].\n   |- Pick two numbers (8, 28) (numbers left: [47]). Try possible operations.\n    |- Try 28 + 8 = 36. Add 36 to the number set. Current number set: [36, 47], target: 11, just two numbers left.\n     |- Try 47 + 36 = 83. Evaluate 83 != 11, drop this branch.\n     |- Try 47 - 36 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 - 36 = 11\nThe step before: 28 + 8 = 36\nThe first step: 45 - 37 = 8\n\nOutput the solution in the required format:\n<Solution>\n45 - 37 = 8\n28 + 8 = 36\n47 - 36 = 11\n<\/Solution>\n","item":{"nums":[37,45,28,47],"solution":["45 - 37 = 8","28 + 8 = 36","47 - 36 = 11"],"target":11}}
+{"instance_id":"countdown_2k_199","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 16, 14, 28]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [12, 16, 14, 28], target: 15. Options for choosing two numbers: [(12, 16), (12, 14), (12, 28), (16, 14), (16, 28), (14, 28)].\n |- Pick two numbers (12, 16) (numbers left: [14, 28]). Try possible operations.\n  |- Try 16 + 12 = 28. Add 28 to the number set. Current number set: [28, 14, 28], target: 15. Options for choosing two numbers: [(28, 14), (28, 28), (14, 28)].\n   |- Pick two numbers (28, 14) (numbers left: [28]). Try possible operations.\n    |- Try 28 + 14 = 42. Add 42 to the number set. Current number set: [42, 28], target: 15, just two numbers left.\n     |- Try 42 + 28 = 70. Evaluate 70 != 15, drop this branch.\n     |- Try 42 - 28 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 42 * 28 = 1176. Evaluate 1176 != 15, drop this branch.\n     |- Try 42 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 28 - 14 = 14. Add 14 to the number set. Current number set: [14, 28], target: 15, just two numbers left.\n     |- Try 28 + 14 = 42. Evaluate 42 != 15, drop this branch.\n     |- Try 28 - 14 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 28 * 14 = 392. Evaluate 392 != 15, drop this branch.\n     |- Try 28 \/ 14 = 2. Evaluate 2 != 15, drop this branch.\n    |- Try 28 * 14 = 392. Add 392 to the number set. Current number set: [392, 28], target: 15, just two numbers left.\n     |- Try 392 + 28 = 420. Evaluate 420 != 15, drop this branch.\n     |- Try 392 - 28 = 364. Evaluate 364 != 15, drop this branch.\n     |- Try 392 * 28 = 10976. 10976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 392 \/ 28 = 14. Evaluate 14 != 15, drop this branch.\n    |- Try 28 \/ 14 = 2. Add 2 to the number set. Current number set: [2, 28], target: 15, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 15, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 15, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 != 15, drop this branch.\n   |- Pick two numbers (28, 28) (numbers left: [14]). Try possible operations.\n    |- Try 28 + 28 = 56. Add 56 to the number set. Current number set: [56, 14], target: 15, just two numbers left.\n     |- Try 56 + 14 = 70. Evaluate 70 != 15, drop this branch.\n     |- Try 56 - 14 = 42. Evaluate 42 != 15, drop this branch.\n     |- Try 56 * 14 = 784. Evaluate 784 != 15, drop this branch.\n     |- Try 56 \/ 14 = 4. Evaluate 4 != 15, drop this branch.\n    |- Try 28 - 28 = 0. Add 0 to the number set. Current number set: [0, 14], target: 15, just two numbers left.\n     |- Try 14 + 0 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 14 - 0 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 14 * 0 = 0. Evaluate 0 != 15, drop this branch.\n     |- Try 14 \/ 0 (invalid operation). drop this branch.\n    |- Try 28 * 28 = 784. Add 784 to the number set. Current number set: [784, 14], target: 15, just two numbers left.\n     |- Try 784 + 14 = 798. Evaluate 798 != 15, drop this branch.\n     |- Try 784 - 14 = 770. Evaluate 770 != 15, drop this branch.\n     |- Try 784 * 14 = 10976. 10976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 784 \/ 14 = 56. Evaluate 56 != 15, drop this branch.\n    |- Try 28 \/ 28 = 1. Add 1 to the number set. Current number set: [1, 14], target: 15, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 14 + 1 = 15\nThe step before: 28 \/ 28 = 1\nThe first step: 16 + 12 = 28\n\nOutput the solution in the required format:\n<Solution>\n16 + 12 = 28\n28 \/ 28 = 1\n14 + 1 = 15\n<\/Solution>\n","item":{"nums":[12,16,14,28],"solution":["16 + 12 = 28","28 \/ 28 = 1","14 + 1 = 15"],"target":15}}