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 5 inhabitants: Lily, Liam, Emma, Amelia, and Avery. According to Lily, "Liam is not a knight". Liam said that If Liam is a knight then Avery is a knave. Emma was heard saying, "Avery is a knight". Amelia expressed that Emma is a knight. In a statement by Avery: "Lily is a knave if and only if Liam 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 Lily is a knight.  No contradiction is found in their claim that Liam is not a knight.
 Liam cannot be a knight, because this would contradict the claim of Lily that Liam is not a knight.
 Liam cannot be a knave, because this would contradict the false claim of their own that If Liam is a knight then Avery is a knave.
 We have exhausted all possibilities for Liam, so let us go back and reconsider Lily.
 Assume Lily is a knave.  No contradiction is found in their false claim that Liam is not a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that If Liam is a knight then Avery is a knave.
 Avery cannot be a knight, because this would contradict the claim of Liam that If Liam is a knight then Avery is a knave.
 Assume Avery is a knave.  No contradiction is found in their false claim that Lily is a knave if and only if Liam is a knave.
 Emma cannot be a knight, because this would contradict the claim of their own that Avery is a knight.
 Assume Emma is a knave.  No contradiction is found in their false claim that Avery is a knight.
 Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knight.
 Assume Amelia is a knave.  No contradiction is found in their false claim that Emma is a knight.
 Therefore, (1) Lily is a knave
 (2) Liam is a knight
 (3) Emma is a knave
 (4) Amelia is a knave
 (5) Avery 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 5 inhabitants: Lily, Liam, Emma, Amelia, and Avery. According to Lily, "Liam is not a knight". Liam said that If Liam is a knight then Avery is a knave. Emma was heard saying, "Avery is a knight". Amelia expressed that Emma is a knight. In a statement by Avery: "Lily is a knave if and only if Liam 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 Lily is a knight. No contradiction is found in their claim that Liam is not a knight.
Liam cannot be a knight, because this would contradict the claim of Lily that Liam is not a knight.
Liam cannot be a knave, because this would contradict the false claim of their own that If Liam is a knight then Avery is a knave.
We have exhausted all possibilities for Liam, so let us go back and reconsider Lily.
Assume Lily is a knave. No contradiction is found in their false claim that Liam is not a knight.
Assume Liam is a knight. No contradiction is found in their claim that If Liam is a knight then Avery is a knave.
Avery cannot be a knight, because this would contradict the claim of Liam that If Liam is a knight then Avery is a knave.
Assume Avery is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Liam is a knave.
Emma cannot be a knight, because this would contradict the claim of their own that Avery is a knight.
Assume Emma is a knave. No contradiction is found in their false claim that Avery is a knight.
Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knight.
Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knight.
Therefore, (1) Lily is a knave
(2) Liam is a knight
(3) Emma is a knave
(4) Amelia is a knave
(5) Avery is a knave </think>
<answer> (1) Lily is a knave
(2) Liam is a knight
(3) Emma is a knave
(4) Amelia is a knave
(5) Avery is a knave </answer>
Lily Liam Emma Amelia Avery
(1) Lily is a knave
(2) Liam is a knight
(3) Emma is a knave
(4) Amelia is a knave
(5) Avery is a knave
(('not', ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 4)), ('telling-truth', 4), ('telling-truth', 2), ('<=>', ('lying', 0), ('lying', 1)))
rule