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: Aiden, Logan, Sebastian, Emma, and Grace. Aiden expressed that Emma is a knave and Grace is a knight. In a statement by Logan: "Sebastian is a knight and Grace is a knave". Sebastian told you that Emma is a knight. "Grace is a knave or Grace is a knight," Emma mentioned. In Grace's words: "Aiden is not 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 Aiden is a knight.  No contradiction is found in their claim that Emma is a knave and Grace is a knight.
 Emma cannot be a knight, because this would contradict the claim of Aiden that Emma is a knave and Grace is a knight.
 Emma cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Grace is a knight.
 We have exhausted all possibilities for Emma, so let us go back and reconsider Aiden.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Emma is a knave and Grace is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that Grace is a knave or Grace is a knight.
 Assume Grace is a knight.  No contradiction is found in their claim that Aiden is not a knight.
 Logan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Grace is a knave.
 Assume Logan is a knave.  No contradiction is found in their false claim that Sebastian is a knight and Grace is a knave.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Emma is a knight.
 Therefore, (1) Aiden is a knave
 (2) Logan is a knave
 (3) Sebastian is a knight
 (4) Emma is a knight
 (5) Grace 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: Aiden, Logan, Sebastian, Emma, and Grace. Aiden expressed that Emma is a knave and Grace is a knight. In a statement by Logan: "Sebastian is a knight and Grace is a knave". Sebastian told you that Emma is a knight. "Grace is a knave or Grace is a knight," Emma mentioned. In Grace's words: "Aiden is not 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 Aiden is a knight. No contradiction is found in their claim that Emma is a knave and Grace is a knight.
Emma cannot be a knight, because this would contradict the claim of Aiden that Emma is a knave and Grace is a knight.
Emma cannot be a knave, because this would contradict the false claim of their own that Grace is a knave or Grace is a knight.
We have exhausted all possibilities for Emma, so let us go back and reconsider Aiden.
Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knave and Grace is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Grace is a knave or Grace is a knight.
Assume Grace is a knight. No contradiction is found in their claim that Aiden is not a knight.
Logan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Grace is a knave.
Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knight and Grace is a knave.
Assume Sebastian is a knight. No contradiction is found in their claim that Emma is a knight.
Therefore, (1) Aiden is a knave
(2) Logan is a knave
(3) Sebastian is a knight
(4) Emma is a knight
(5) Grace is a knight </think>
<answer> (1) Aiden is a knave
(2) Logan is a knave
(3) Sebastian is a knight
(4) Emma is a knight
(5) Grace is a knight </answer>
Aiden Logan Sebastian Emma Grace
(1) Aiden is a knave
(2) Logan is a knave
(3) Sebastian is a knight
(4) Emma is a knight
(5) Grace is a knight
(('and', ('lying', 3), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('lying', 4)), ('telling-truth', 3), ('or', ('lying', 4), ('telling-truth', 4)), ('not', ('telling-truth', 0)))
rule