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: Lily, Oliver, William, Amelia, Ella, and Jacob. Lily remarked, "If William is a knave then William is a knight". "Jacob is not a knight" - Oliver. In a statement by William: "If Amelia is a knight then Oliver is a knight". Amelia told you that William is a knight if and only if Oliver is a knight. In a statement by Ella: "William is not a knave". Jacob stated, "Ella is not a knave". 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 Lily is a knight.  No contradiction is found in their claim that If William is a knave then William is a knight.
 Assume William is a knight.  No contradiction is found in their claim that If Amelia is a knight then Oliver is a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that William is a knight if and only if Oliver is a knight.
 Assume Oliver is a knight.  No contradiction is found in their claim that Jacob is not a knight.
 Jacob cannot be a knight, because this would contradict the claim of Oliver that Jacob is not a knight.
 Assume Jacob is a knave.  No contradiction is found in their false claim that Ella is not a knave.
 Ella cannot be a knight, because this would contradict the false claim of Jacob that Ella is not a knave.
 Ella cannot be a knave, because this would contradict the false claim of their own that William is not a knave.
 We have exhausted all possibilities for Ella and Jacob, so let us go back and reconsider Oliver.
 Oliver cannot be a knave, because this would contradict the claim of William that If Amelia is a knight then Oliver is a knight.
 We have exhausted all possibilities for Oliver, so let us go back and reconsider Amelia.
 Assume Amelia is a knave.  No contradiction is found in their false claim that William is a knight if and only if Oliver is a knight.
 Oliver cannot be a knight, because this would contradict the false claim of Amelia that William is a knight if and only if Oliver is a knight.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Jacob is not a knight.
 Assume Jacob is a knight.  No contradiction is found in their claim that Ella is not a knave.
 Assume Ella is a knight.  No contradiction is found in their claim that William is not a knave.
 Therefore, (1) Lily is a knight
 (2) Oliver is a knave
 (3) William is a knight
 (4) Amelia is a knave
 (5) Ella is a knight
 (6) Jacob is a knight
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: Lily, Oliver, William, Amelia, Ella, and Jacob. Lily remarked, "If William is a knave then William is a knight". "Jacob is not a knight" - Oliver. In a statement by William: "If Amelia is a knight then Oliver is a knight". Amelia told you that William is a knight if and only if Oliver is a knight. In a statement by Ella: "William is not a knave". Jacob stated, "Ella is not a knave". 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 Lily is a knight. No contradiction is found in their claim that If William is a knave then William is a knight.
Assume William is a knight. No contradiction is found in their claim that If Amelia is a knight then Oliver is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that William is a knight if and only if Oliver is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Jacob is not a knight.
Jacob cannot be a knight, because this would contradict the claim of Oliver that Jacob is not a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Ella is not a knave.
Ella cannot be a knight, because this would contradict the false claim of Jacob that Ella is not a knave.
Ella cannot be a knave, because this would contradict the false claim of their own that William is not a knave.
We have exhausted all possibilities for Ella and Jacob, so let us go back and reconsider Oliver.
Oliver cannot be a knave, because this would contradict the claim of William that If Amelia is a knight then Oliver is a knight.
We have exhausted all possibilities for Oliver, so let us go back and reconsider Amelia.
Assume Amelia is a knave. No contradiction is found in their false claim that William is a knight if and only if Oliver is a knight.
Oliver cannot be a knight, because this would contradict the false claim of Amelia that William is a knight if and only if Oliver is a knight.
Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is not a knight.
Assume Jacob is a knight. No contradiction is found in their claim that Ella is not a knave.
Assume Ella is a knight. No contradiction is found in their claim that William is not a knave.
Therefore, (1) Lily is a knight
(2) Oliver is a knave
(3) William is a knight
(4) Amelia is a knave
(5) Ella is a knight
(6) Jacob is a knight </think>
<answer> (1) Lily is a knight
(2) Oliver is a knave
(3) William is a knight
(4) Amelia is a knave
(5) Ella is a knight
(6) Jacob is a knight </answer>
Lily Oliver William Amelia Ella Jacob
(1) Lily is a knight
(2) Oliver is a knave
(3) William is a knight
(4) Amelia is a knave
(5) Ella is a knight
(6) Jacob is a knight
(('->', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('lying', 2)), ('not', ('lying', 4)))
rule