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: Ava, David, and Zoey. In a statement by Ava: "David is a knave". David stated, "David is a knight if and only if Ava is a knight". Zoey commented, "If David is a knight then 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 David is a knave.
 David cannot be a knight, because this would contradict the claim of Ava that David is a knave.
 Assume David is a knave.  No contradiction is found in their false claim that David is a knight if and only if Ava is a knight.
 Assume Zoey is a knight.  No contradiction is found in their claim that If David is a knight then Ava is a knight.
 Therefore, (1) Ava is a knight
 (2) David is a knave
 (3) 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 3 inhabitants: Ava, David, and Zoey. In a statement by Ava: "David is a knave". David stated, "David is a knight if and only if Ava is a knight". Zoey commented, "If David is a knight then 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 David is a knave.
David cannot be a knight, because this would contradict the claim of Ava that David is a knave.
Assume David is a knave. No contradiction is found in their false claim that David is a knight if and only if Ava is a knight.
Assume Zoey is a knight. No contradiction is found in their claim that If David is a knight then Ava is a knight.
Therefore, (1) Ava is a knight
(2) David is a knave
(3) Zoey is a knight </think>
<answer> (1) Ava is a knight
(2) David is a knave
(3) Zoey is a knight </answer>
Ava David Zoey
(1) Ava is a knight
(2) David is a knave
(3) Zoey is a knight
(('lying', 1), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)))
rule