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, Grace, Zoey, Sebastian, and Harper. Luke said, "Sebastian is a knight if and only if Zoey is a knave." In Grace's words: "If Zoey is a knave then Zoey is a knight". Zoey commented, "Sebastian is a knight if and only if Zoey is a knight". Sebastian commented, "Harper is a knave if and only if Sebastian is a knight". Harper said that Grace 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 Sebastian is a knight if and only if Zoey is a knave.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Harper is a knave if and only if Sebastian is a knight.
 Harper cannot be a knight, because this would contradict the claim of Sebastian that Harper is a knave if and only if Sebastian is a knight.
 Assume Harper is a knave.  No contradiction is found in their false claim that Grace is a knight.
 Grace cannot be a knight, because this would contradict the false claim of Harper that Grace is a knight.
 Assume Grace is a knave.  No contradiction is found in their false claim that If Zoey is a knave then Zoey is a knight.
 Zoey cannot be a knight, because this would contradict the claim of Luke that Sebastian is a knight if and only if Zoey is a knave.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Sebastian is a knight if and only if Zoey is a knight.
 Therefore, (1) Luke is a knight
 (2) Grace is a knave
 (3) Zoey is a knave
 (4) Sebastian is a knight
 (5) Harper 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: Luke, Grace, Zoey, Sebastian, and Harper. Luke said, "Sebastian is a knight if and only if Zoey is a knave." In Grace's words: "If Zoey is a knave then Zoey is a knight". Zoey commented, "Sebastian is a knight if and only if Zoey is a knight". Sebastian commented, "Harper is a knave if and only if Sebastian is a knight". Harper said that Grace 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 Sebastian is a knight if and only if Zoey is a knave.
Assume Sebastian is a knight. No contradiction is found in their claim that Harper is a knave if and only if Sebastian is a knight.
Harper cannot be a knight, because this would contradict the claim of Sebastian that Harper is a knave if and only if Sebastian is a knight.
Assume Harper is a knave. No contradiction is found in their false claim that Grace is a knight.
Grace cannot be a knight, because this would contradict the false claim of Harper that Grace is a knight.
Assume Grace is a knave. No contradiction is found in their false claim that If Zoey is a knave then Zoey is a knight.
Zoey cannot be a knight, because this would contradict the claim of Luke that Sebastian is a knight if and only if Zoey is a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Zoey is a knight.
Therefore, (1) Luke is a knight
(2) Grace is a knave
(3) Zoey is a knave
(4) Sebastian is a knight
(5) Harper is a knave </think>
<answer> (1) Luke is a knight
(2) Grace is a knave
(3) Zoey is a knave
(4) Sebastian is a knight
(5) Harper is a knave </answer>
Luke Grace Zoey Sebastian Harper
(1) Luke is a knight
(2) Grace is a knave
(3) Zoey is a knave
(4) Sebastian is a knight
(5) Harper is a knave
(('<=>', ('telling-truth', 3), ('lying', 2)), ('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('telling-truth', 1))
rule