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: Luke, Michael, Jackson, Emma, and Zoey. In Luke's words: "Zoey is a knave". According to Michael, "If Luke is a knave then Michael is a knight". Jackson remarked, "Zoey is a knave if and only if Luke is a knight". Emma said, "Michael is a knight and Zoey is a knave." Zoey told you that If Michael is a knight then Emma 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 Luke is a knight.  No contradiction is found in their claim that Zoey is a knave.
 Zoey cannot be a knight, because this would contradict the claim of Luke that Zoey is a knave.
 Assume Zoey is a knave.  No contradiction is found in their false claim that If Michael is a knight then Emma is a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that If Luke is a knave then Michael is a knight.
 Emma cannot be a knight, because this would contradict the false claim of Zoey that If Michael is a knight then Emma is a knight.
 Emma cannot be a knave, because this would contradict the false claim of their own that Michael is a knight and Zoey is a knave.
 We have exhausted all possibilities for Emma, so let us go back and reconsider Michael.
 Michael cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Michael is a knight.
 We have exhausted all possibilities for Michael and Zoey, so let us go back and reconsider Luke.
 Assume Luke is a knave.  No contradiction is found in their false claim that Zoey is a knave.
 Assume Zoey is a knight.  No contradiction is found in their claim that If Michael is a knight then Emma is a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that If Luke is a knave then Michael is a knight.
 Emma cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Zoey is a knave.
 Emma cannot be a knave, because this would contradict the claim of Zoey that If Michael is a knight then Emma is a knight.
 We have exhausted all possibilities for Emma, so let us go back and reconsider Michael.
 Assume Michael is a knave.  No contradiction is found in their false claim that If Luke is a knave then Michael is a knight.
 Emma cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Zoey is a knave.
 Assume Emma is a knave.  No contradiction is found in their false claim that Michael is a knight and Zoey is a knave.
 Assume Jackson is a knight.  No contradiction is found in their claim that Zoey is a knave if and only if Luke is a knight.
 Therefore, (1) Luke is a knave
 (2) Michael is a knave
 (3) Jackson is a knight
 (4) Emma is a knave
 (5) Zoey 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: Luke, Michael, Jackson, Emma, and Zoey. In Luke's words: "Zoey is a knave". According to Michael, "If Luke is a knave then Michael is a knight". Jackson remarked, "Zoey is a knave if and only if Luke is a knight". Emma said, "Michael is a knight and Zoey is a knave." Zoey told you that If Michael is a knight then Emma 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 Luke is a knight. No contradiction is found in their claim that Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of Luke that Zoey is a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that If Michael is a knight then Emma is a knight.
Assume Michael is a knight. No contradiction is found in their claim that If Luke is a knave then Michael is a knight.
Emma cannot be a knight, because this would contradict the false claim of Zoey that If Michael is a knight then Emma is a knight.
Emma cannot be a knave, because this would contradict the false claim of their own that Michael is a knight and Zoey is a knave.
We have exhausted all possibilities for Emma, so let us go back and reconsider Michael.
Michael cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Michael is a knight.
We have exhausted all possibilities for Michael and Zoey, so let us go back and reconsider Luke.
Assume Luke is a knave. No contradiction is found in their false claim that Zoey is a knave.
Assume Zoey is a knight. No contradiction is found in their claim that If Michael is a knight then Emma is a knight.
Assume Michael is a knight. No contradiction is found in their claim that If Luke is a knave then Michael is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Zoey is a knave.
Emma cannot be a knave, because this would contradict the claim of Zoey that If Michael is a knight then Emma is a knight.
We have exhausted all possibilities for Emma, so let us go back and reconsider Michael.
Assume Michael is a knave. No contradiction is found in their false claim that If Luke is a knave then Michael is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Zoey is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Michael is a knight and Zoey is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Luke is a knight.
Therefore, (1) Luke is a knave
(2) Michael is a knave
(3) Jackson is a knight
(4) Emma is a knave
(5) Zoey is a knight </think>
<answer> (1) Luke is a knave
(2) Michael is a knave
(3) Jackson is a knight
(4) Emma is a knave
(5) Zoey is a knight </answer>
Luke Michael Jackson Emma Zoey
(1) Luke is a knave
(2) Michael is a knave
(3) Jackson is a knight
(4) Emma is a knave
(5) Zoey is a knight
(('lying', 4), ('->', ('lying', 0), ('telling-truth', 1)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 4)), ('->', ('telling-truth', 1), ('telling-truth', 3)))
rule