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 4 inhabitants: Ella, Oliver, Aurora, and Michael. "If Oliver is a knave then Ella is a knight," Ella mentioned. In Oliver's words: "Michael is a knight". In Aurora's words: "Michael is a knave and Oliver is a knight". According to Michael, "If Aurora is a knave then Ella is 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 Ella is a knight.  No contradiction is found in their claim that If Oliver is a knave then Ella is a knight.
 Assume Oliver is a knight.  No contradiction is found in their claim that Michael is a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that If Aurora is a knave then Ella is a knave.
 Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Oliver is a knight.
 Aurora cannot be a knave, because this would contradict the claim of Michael that If Aurora is a knave then Ella is a knave.
 We have exhausted all possibilities for Aurora, so let us go back and reconsider Michael.
 Michael cannot be a knave, because this would contradict the claim of Oliver that Michael is a knight.
 We have exhausted all possibilities for Michael, so let us go back and reconsider Oliver.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Michael is a knight.
 Michael cannot be a knight, because this would contradict the false claim of Oliver that Michael is a knight.
 Assume Michael is a knave.  No contradiction is found in their false claim that If Aurora is a knave then Ella is a knave.
 Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Oliver is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Michael is a knave and Oliver is a knight.
 Therefore, (1) Ella is a knight
 (2) Oliver is a knave
 (3) Aurora is a knave
 (4) Michael 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 4 inhabitants: Ella, Oliver, Aurora, and Michael. "If Oliver is a knave then Ella is a knight," Ella mentioned. In Oliver's words: "Michael is a knight". In Aurora's words: "Michael is a knave and Oliver is a knight". According to Michael, "If Aurora is a knave then Ella is 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 Ella is a knight. No contradiction is found in their claim that If Oliver is a knave then Ella is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Michael is a knight.
Assume Michael is a knight. No contradiction is found in their claim that If Aurora is a knave then Ella is a knave.
Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Oliver is a knight.
Aurora cannot be a knave, because this would contradict the claim of Michael that If Aurora is a knave then Ella is a knave.
We have exhausted all possibilities for Aurora, so let us go back and reconsider Michael.
Michael cannot be a knave, because this would contradict the claim of Oliver that Michael is a knight.
We have exhausted all possibilities for Michael, so let us go back and reconsider Oliver.
Assume Oliver is a knave. No contradiction is found in their false claim that Michael is a knight.
Michael cannot be a knight, because this would contradict the false claim of Oliver that Michael is a knight.
Assume Michael is a knave. No contradiction is found in their false claim that If Aurora is a knave then Ella is a knave.
Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Oliver is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knave and Oliver is a knight.
Therefore, (1) Ella is a knight
(2) Oliver is a knave
(3) Aurora is a knave
(4) Michael is a knave </think>
<answer> (1) Ella is a knight
(2) Oliver is a knave
(3) Aurora is a knave
(4) Michael is a knave </answer>
Ella Oliver Aurora Michael
(1) Ella is a knight
(2) Oliver is a knave
(3) Aurora is a knave
(4) Michael is a knave
(('->', ('lying', 1), ('telling-truth', 0)), ('telling-truth', 3), ('and', ('lying', 3), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 0)))
rule