A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Oliver, Owen, Emma, Aurora, and Jackson. In a statement by Daniel: "If Owen is a knave then Jackson is a knight". In Oliver's words: "Jackson is a knight if and only if Aurora is a knight". In a statement by Owen: "Emma is a knave". In a statement by Emma: "Daniel is a knave and Jackson is a knave". According to Aurora, "Daniel is a knave if and only if Jackson is a knave". Jackson noted, "Oliver is not a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
user
Assume Daniel is a knight.  No contradiction is found in their claim that If Owen is a knave then Jackson is a knight.
 Assume Owen is a knight.  No contradiction is found in their claim that Emma is a knave.
 Emma cannot be a knight, because this would contradict the claim of Owen that Emma is a knave.
 Assume Emma is a knave.  No contradiction is found in their false claim that Daniel is a knave and Jackson is a knave.
 Assume Jackson is a knight.  No contradiction is found in their claim that Oliver is not a knight.
 Oliver cannot be a knight, because this would contradict the claim of Jackson that Oliver is not a knight.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Jackson is a knight if and only if Aurora is a knight.
 Aurora cannot be a knight, because this would contradict the false claim of Oliver that Jackson is a knight if and only if Aurora is a knight.
 Aurora cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave if and only if Jackson is a knave.
 We have exhausted all possibilities for Aurora and Oliver, so let us go back and reconsider Jackson.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Oliver is not a knight.
 Assume Oliver is a knight.  No contradiction is found in their claim that Jackson is a knight if and only if Aurora is a knight.
 Aurora cannot be a knight, because this would contradict the claim of Oliver that Jackson is a knight if and only if Aurora is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Daniel is a knave if and only if Jackson is a knave.
 Therefore, (1) Daniel is a knight
 (2) Oliver is a knight
 (3) Owen is a knight
 (4) Emma is a knave
 (5) Aurora is a knave
 (6) Jackson is a knave
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Oliver, Owen, Emma, Aurora, and Jackson. In a statement by Daniel: "If Owen is a knave then Jackson is a knight". In Oliver's words: "Jackson is a knight if and only if Aurora is a knight". In a statement by Owen: "Emma is a knave". In a statement by Emma: "Daniel is a knave and Jackson is a knave". According to Aurora, "Daniel is a knave if and only if Jackson is a knave". Jackson noted, "Oliver is not a knight". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
Assume Daniel is a knight. No contradiction is found in their claim that If Owen is a knave then Jackson is a knight.
Assume Owen is a knight. No contradiction is found in their claim that Emma is a knave.
Emma cannot be a knight, because this would contradict the claim of Owen that Emma is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Daniel is a knave and Jackson is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that Oliver is not a knight.
Oliver cannot be a knight, because this would contradict the claim of Jackson that Oliver is not a knight.
Assume Oliver is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Aurora is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Oliver that Jackson is a knight if and only if Aurora is a knight.
Aurora cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave if and only if Jackson is a knave.
We have exhausted all possibilities for Aurora and Oliver, so let us go back and reconsider Jackson.
Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is not a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aurora is a knight.
Aurora cannot be a knight, because this would contradict the claim of Oliver that Jackson is a knight if and only if Aurora is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Jackson is a knave.
Therefore, (1) Daniel is a knight
(2) Oliver is a knight
(3) Owen is a knight
(4) Emma is a knave
(5) Aurora is a knave
(6) Jackson is a knave </think>
<answer> (1) Daniel is a knight
(2) Oliver is a knight
(3) Owen is a knight
(4) Emma is a knave
(5) Aurora is a knave
(6) Jackson is a knave </answer>
Daniel Oliver Owen Emma Aurora Jackson
(1) Daniel is a knight
(2) Oliver is a knight
(3) Owen is a knight
(4) Emma is a knave
(5) Aurora is a knave
(6) Jackson is a knave
(('->', ('lying', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('lying', 3), ('and', ('lying', 0), ('lying', 5)), ('<=>', ('lying', 0), ('lying', 5)), ('not', ('telling-truth', 1)))
rule