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