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: Avery, Oliver, and Scarlett. Avery told you that Scarlett is a knight if and only if Scarlett is a knave. In Oliver's words: "Avery is a knave and Scarlett is a knight". Scarlett expressed that Oliver is a knave and Scarlett 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
Avery cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Scarlett is a knave.
 Assume Avery is a knave.  No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave.
 Assume Scarlett is a knight.  No contradiction is found in their claim that Oliver is a knave and Scarlett is a knight.
 Oliver cannot be a knight, because this would contradict the claim of Scarlett that Oliver is a knave and Scarlett is a knight.
 Oliver cannot be a knave, because this would contradict the false claim of their own that Avery is a knave and Scarlett is a knight.
 We have exhausted all possibilities for Oliver, so let us go back and reconsider Scarlett.
 Assume Scarlett is a knave.  No contradiction is found in their false claim that Oliver is a knave and Scarlett is a knight.
 Oliver cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Scarlett is a knight.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Avery is a knave and Scarlett is a knight.
 Therefore, (1) Avery is a knave
 (2) Oliver is a knave
 (3) Scarlett 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: Avery, Oliver, and Scarlett. Avery told you that Scarlett is a knight if and only if Scarlett is a knave. In Oliver's words: "Avery is a knave and Scarlett is a knight". Scarlett expressed that Oliver is a knave and Scarlett 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> 
Avery cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight if and only if Scarlett is a knave.
Assume Avery is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave.
Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knave and Scarlett is a knight.
Oliver cannot be a knight, because this would contradict the claim of Scarlett that Oliver is a knave and Scarlett is a knight.
Oliver cannot be a knave, because this would contradict the false claim of their own that Avery is a knave and Scarlett is a knight.
We have exhausted all possibilities for Oliver, so let us go back and reconsider Scarlett.
Assume Scarlett is a knave. No contradiction is found in their false claim that Oliver is a knave and Scarlett is a knight.
Oliver cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Scarlett is a knight.
Assume Oliver is a knave. No contradiction is found in their false claim that Avery is a knave and Scarlett is a knight.
Therefore, (1) Avery is a knave
(2) Oliver is a knave
(3) Scarlett is a knave </think>
<answer> (1) Avery is a knave
(2) Oliver is a knave
(3) Scarlett is a knave </answer>
Avery Oliver Scarlett
(1) Avery is a knave
(2) Oliver is a knave
(3) Scarlett is a knave
(('<=>', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 2)))
rule