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