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 3 inhabitants: Luke, Michael, and Zoey. "Michael is a knight," Luke mentioned. "If Michael is a knight then Zoey is a knave," Michael mentioned. "Luke is not a knight," Zoey claimed. 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 Luke 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 Michael is a knight then Zoey is a knave.
 Zoey cannot be a knight, because this would contradict the claim of Michael that If Michael is a knight then Zoey is a knave.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Luke is not a knight.
 Therefore, (1) Luke is a knight
 (2) Michael is a knight
 (3) Zoey 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 3 inhabitants: Luke, Michael, and Zoey. "Michael is a knight," Luke mentioned. "If Michael is a knight then Zoey is a knave," Michael mentioned. "Luke is not a knight," Zoey claimed. 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 Luke 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 Michael is a knight then Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of Michael that If Michael is a knight then Zoey is a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that Luke is not a knight.
Therefore, (1) Luke is a knight
(2) Michael is a knight
(3) Zoey is a knave </think>
<answer> (1) Luke is a knight
(2) Michael is a knight
(3) Zoey is a knave </answer>
Luke Michael Zoey
(1) Luke is a knight
(2) Michael is a knight
(3) Zoey is a knave
(('telling-truth', 1), ('->', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 0)))
rule