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 3 inhabitants: Riley, Grace, and Zoey. Riley stated, "Zoey is a knight if and only if Zoey is a knave". Grace told you that Zoey is a knight or Riley is a knight. As Zoey put it, "Grace is a knave and 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
Riley cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Zoey is a knave.
 Assume Riley is a knave.  No contradiction is found in their false claim that Zoey is a knight if and only if Zoey is a knave.
 Zoey cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Grace is a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Grace is a knave and Grace is a knight.
 Grace cannot be a knight, because this would contradict the claim of their own that Zoey is a knight or Riley is a knight.
 Assume Grace is a knave.  No contradiction is found in their false claim that Zoey is a knight or Riley is a knight.
 Therefore, (1) Riley is a knave
 (2) Grace is a knave
 (3) Zoey 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 3 inhabitants: Riley, Grace, and Zoey. Riley stated, "Zoey is a knight if and only if Zoey is a knave". Grace told you that Zoey is a knight or Riley is a knight. As Zoey put it, "Grace is a knave and 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> 
Riley cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Zoey is a knave.
Assume Riley is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Zoey is a knave.
Zoey cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Grace is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Grace is a knave and Grace is a knight.
Grace cannot be a knight, because this would contradict the claim of their own that Zoey is a knight or Riley is a knight.
Assume Grace is a knave. No contradiction is found in their false claim that Zoey is a knight or Riley is a knight.
Therefore, (1) Riley is a knave
(2) Grace is a knave
(3) Zoey is a knave </think>
<answer> (1) Riley is a knave
(2) Grace is a knave
(3) Zoey is a knave </answer>
Riley Grace Zoey
(1) Riley is a knave
(2) Grace is a knave
(3) Zoey is a knave
(('<=>', ('telling-truth', 2), ('lying', 2)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 1)))
rule