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: Scarlett, Avery, and Emma. "Avery is a knave if and only if Emma is a knave," Scarlett claimed. Avery said, "Emma is a knight." Emma stated, "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
Assume Scarlett is a knight.  No contradiction is found in their claim that Avery is a knave if and only if Emma is a knave.
 Assume Avery is a knight.  No contradiction is found in their claim that Emma is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that Scarlett is a knight.
 Therefore, (1) Scarlett is a knight
 (2) Avery is a knight
 (3) Emma 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: Scarlett, Avery, and Emma. "Avery is a knave if and only if Emma is a knave," Scarlett claimed. Avery said, "Emma is a knight." Emma stated, "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> 
Assume Scarlett is a knight. No contradiction is found in their claim that Avery is a knave if and only if Emma is a knave.
Assume Avery is a knight. No contradiction is found in their claim that Emma is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knight.
Therefore, (1) Scarlett is a knight
(2) Avery is a knight
(3) Emma is a knight </think>
<answer> (1) Scarlett is a knight
(2) Avery is a knight
(3) Emma is a knight </answer>
Scarlett Avery Emma
(1) Scarlett is a knight
(2) Avery is a knight
(3) Emma is a knight
(('<=>', ('lying', 1), ('lying', 2)), ('telling-truth', 2), ('telling-truth', 0))
rule