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: Avery, Aiden, Emma, and Lucas. Avery asserted: "Lucas is a knave and Emma is a knave". "Lucas is not a knight" - Aiden. Emma noted, "Avery is a knave". As Lucas put it, "Emma is a knight if and only if Avery 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 Lucas is a knave and Emma is a knave.
 Lucas cannot be a knight, because this would contradict the claim of Avery that Lucas is a knave and Emma is a knave.
 Assume Lucas is a knave.  No contradiction is found in their false claim that Emma is a knight if and only if Avery is a knave.
 Emma cannot be a knight, because this would contradict the claim of Avery that Lucas is a knave and Emma is a knave.
 Emma cannot be a knave, because this would contradict the false claim of Lucas that Emma is a knight if and only if Avery is a knave.
 We have exhausted all possibilities for Emma and Lucas, so let us go back and reconsider Avery.
 Assume Avery is a knave.  No contradiction is found in their false claim that Lucas is a knave and Emma is a knave.
 Assume Lucas is a knight.  No contradiction is found in their claim that Emma is a knight if and only if Avery is a knave.
 Assume Emma is a knight.  No contradiction is found in their claim that Avery is a knave.
 Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Lucas is not a knight.
 Therefore, (1) Avery is a knave
 (2) Aiden is a knave
 (3) Emma is a knight
 (4) Lucas 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 4 inhabitants: Avery, Aiden, Emma, and Lucas. Avery asserted: "Lucas is a knave and Emma is a knave". "Lucas is not a knight" - Aiden. Emma noted, "Avery is a knave". As Lucas put it, "Emma is a knight if and only if Avery 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 Lucas is a knave and Emma is a knave.
Lucas cannot be a knight, because this would contradict the claim of Avery that Lucas is a knave and Emma is a knave.
Assume Lucas is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Avery is a knave.
Emma cannot be a knight, because this would contradict the claim of Avery that Lucas is a knave and Emma is a knave.
Emma cannot be a knave, because this would contradict the false claim of Lucas that Emma is a knight if and only if Avery is a knave.
We have exhausted all possibilities for Emma and Lucas, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that Lucas is a knave and Emma is a knave.
Assume Lucas is a knight. No contradiction is found in their claim that Emma is a knight if and only if Avery is a knave.
Assume Emma is a knight. No contradiction is found in their claim that Avery is a knave.
Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that Lucas is not a knight.
Therefore, (1) Avery is a knave
(2) Aiden is a knave
(3) Emma is a knight
(4) Lucas is a knight </think>
<answer> (1) Avery is a knave
(2) Aiden is a knave
(3) Emma is a knight
(4) Lucas is a knight </answer>
Avery Aiden Emma Lucas
(1) Avery is a knave
(2) Aiden is a knave
(3) Emma is a knight
(4) Lucas is a knight
(('and', ('lying', 3), ('lying', 2)), ('not', ('telling-truth', 3)), ('lying', 0), ('<=>', ('telling-truth', 2), ('lying', 0)))
rule