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 6 inhabitants: Ava, Mia, Evelyn, Jack, Logan, and Lily. Ava told you that Jack is a knight if and only if Evelyn is a knave. Mia commented, "Ava is not a knight". Evelyn remarked, "Ava is a knight if and only if Mia is a knave". Jack stated, "Mia is a knave and Ava is a knave". Logan said, "If Lily is a knight then Evelyn is a knave." Lily stated, "Mia 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 Ava is a knight.  No contradiction is found in their claim that Jack is a knight if and only if Evelyn is a knave.
 Jack cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Ava is a knave.
 Assume Jack is a knave.  No contradiction is found in their false claim that Mia is a knave and Ava is a knave.
 Mia cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.
 Assume Mia is a knave.  No contradiction is found in their false claim that Ava is not a knight.
 Assume Evelyn is a knight.  No contradiction is found in their claim that Ava is a knight if and only if Mia is a knave.
 Assume Logan is a knight.  No contradiction is found in their claim that If Lily is a knight then Evelyn is a knave.
 Lily cannot be a knight, because this would contradict the claim of Logan that If Lily is a knight then Evelyn is a knave.
 Lily cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.
 We have exhausted all possibilities for Lily, so let us go back and reconsider Logan.
 Assume Logan is a knave.  No contradiction is found in their false claim that If Lily is a knight then Evelyn is a knave.
 Assume Lily is a knight.  No contradiction is found in their claim that Mia is a knave.
 Therefore, (1) Ava is a knight
 (2) Mia is a knave
 (3) Evelyn is a knight
 (4) Jack is a knave
 (5) Logan is a knave
 (6) Lily 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 6 inhabitants: Ava, Mia, Evelyn, Jack, Logan, and Lily. Ava told you that Jack is a knight if and only if Evelyn is a knave. Mia commented, "Ava is not a knight". Evelyn remarked, "Ava is a knight if and only if Mia is a knave". Jack stated, "Mia is a knave and Ava is a knave". Logan said, "If Lily is a knight then Evelyn is a knave." Lily stated, "Mia 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 Ava is a knight. No contradiction is found in their claim that Jack is a knight if and only if Evelyn is a knave.
Jack cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Ava is a knave.
Assume Jack is a knave. No contradiction is found in their false claim that Mia is a knave and Ava is a knave.
Mia cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.
Assume Mia is a knave. No contradiction is found in their false claim that Ava is not a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Ava is a knight if and only if Mia is a knave.
Assume Logan is a knight. No contradiction is found in their claim that If Lily is a knight then Evelyn is a knave.
Lily cannot be a knight, because this would contradict the claim of Logan that If Lily is a knight then Evelyn is a knave.
Lily cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.
We have exhausted all possibilities for Lily, so let us go back and reconsider Logan.
Assume Logan is a knave. No contradiction is found in their false claim that If Lily is a knight then Evelyn is a knave.
Assume Lily is a knight. No contradiction is found in their claim that Mia is a knave.
Therefore, (1) Ava is a knight
(2) Mia is a knave
(3) Evelyn is a knight
(4) Jack is a knave
(5) Logan is a knave
(6) Lily is a knight </think>
<answer> (1) Ava is a knight
(2) Mia is a knave
(3) Evelyn is a knight
(4) Jack is a knave
(5) Logan is a knave
(6) Lily is a knight </answer>
Ava Mia Evelyn Jack Logan Lily
(1) Ava is a knight
(2) Mia is a knave
(3) Evelyn is a knight
(4) Jack is a knave
(5) Logan is a knave
(6) Lily is a knight
(('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 1), ('lying', 0)), ('->', ('telling-truth', 5), ('lying', 2)), ('lying', 1))
rule