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: Ava, Joseph, Michael, Luke, and Daniel. Ava commented, "Michael is not a knight". Joseph commented, "Ava is not a knave". In Michael's words: "If Luke is a knave then Ava is a knight". As Luke put it, "If Luke is a knight then Ava is a knave". Daniel commented, "Michael is a knight or Ava is a knight". 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 Michael is not a knight.
 Michael cannot be a knight, because this would contradict the claim of Ava that Michael is not a knight.
 Michael cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Ava is a knight.
 We have exhausted all possibilities for Michael, so let us go back and reconsider Ava.
 Assume Ava is a knave.  No contradiction is found in their false claim that Michael is not a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that If Luke is a knave then Ava is a knight.
 Assume Luke is a knight.  No contradiction is found in their claim that If Luke is a knight then Ava is a knave.
 Joseph cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.
 Assume Joseph is a knave.  No contradiction is found in their false claim that Ava is not a knave.
 Assume Daniel is a knight.  No contradiction is found in their claim that Michael is a knight or Ava is a knight.
 Therefore, (1) Ava is a knave
 (2) Joseph is a knave
 (3) Michael is a knight
 (4) Luke is a knight
 (5) Daniel 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 5 inhabitants: Ava, Joseph, Michael, Luke, and Daniel. Ava commented, "Michael is not a knight". Joseph commented, "Ava is not a knave". In Michael's words: "If Luke is a knave then Ava is a knight". As Luke put it, "If Luke is a knight then Ava is a knave". Daniel commented, "Michael is a knight or Ava is a knight". 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 Michael is not a knight.
Michael cannot be a knight, because this would contradict the claim of Ava that Michael is not a knight.
Michael cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Ava is a knight.
We have exhausted all possibilities for Michael, so let us go back and reconsider Ava.
Assume Ava is a knave. No contradiction is found in their false claim that Michael is not a knight.
Assume Michael is a knight. No contradiction is found in their claim that If Luke is a knave then Ava is a knight.
Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Ava is a knave.
Joseph cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.
Assume Joseph is a knave. No contradiction is found in their false claim that Ava is not a knave.
Assume Daniel is a knight. No contradiction is found in their claim that Michael is a knight or Ava is a knight.
Therefore, (1) Ava is a knave
(2) Joseph is a knave
(3) Michael is a knight
(4) Luke is a knight
(5) Daniel is a knight </think>
<answer> (1) Ava is a knave
(2) Joseph is a knave
(3) Michael is a knight
(4) Luke is a knight
(5) Daniel is a knight </answer>
Ava Joseph Michael Luke Daniel
(1) Ava is a knave
(2) Joseph is a knave
(3) Michael is a knight
(4) Luke is a knight
(5) Daniel is a knight
(('not', ('telling-truth', 2)), ('not', ('lying', 0)), ('->', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 0)), ('or', ('telling-truth', 2), ('telling-truth', 0)))
rule