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