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 6 inhabitants: Owen, Riley, Sofia, Michael, Grace, and Avery. Owen stated, "Michael is a knight if and only if Sofia is a knight". Riley commented, "Sofia is a knight and Avery is a knight". Sofia noted, "Riley is a knave or Michael is a knight". Michael remarked, "If Avery is a knight then Riley is a knight". "If Sofia is a knave then Riley is a knave" - Grace. According to Avery, "Michael is a knave if and only if Sofia is a knave". 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 Owen is a knight.  No contradiction is found in their claim that Michael is a knight if and only if Sofia is a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that If Avery is a knight then Riley is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Michael is a knave if and only if Sofia is a knave.
 Assume Sofia is a knight.  No contradiction is found in their claim that Riley is a knave or Michael is a knight.
 Assume Riley is a knight.  No contradiction is found in their claim that Sofia is a knight and Avery is a knight.
 Assume Grace is a knight.  No contradiction is found in their claim that If Sofia is a knave then Riley is a knave.
 Therefore, (1) Owen is a knight
 (2) Riley is a knight
 (3) Sofia is a knight
 (4) Michael is a knight
 (5) Grace is a knight
 (6) Avery 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 6 inhabitants: Owen, Riley, Sofia, Michael, Grace, and Avery. Owen stated, "Michael is a knight if and only if Sofia is a knight". Riley commented, "Sofia is a knight and Avery is a knight". Sofia noted, "Riley is a knave or Michael is a knight". Michael remarked, "If Avery is a knight then Riley is a knight". "If Sofia is a knave then Riley is a knave" - Grace. According to Avery, "Michael is a knave if and only if Sofia is a knave". 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 Owen is a knight. No contradiction is found in their claim that Michael is a knight if and only if Sofia is a knight.
Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knight then Riley is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Michael is a knave if and only if Sofia is a knave.
Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knave or Michael is a knight.
Assume Riley is a knight. No contradiction is found in their claim that Sofia is a knight and Avery is a knight.
Assume Grace is a knight. No contradiction is found in their claim that If Sofia is a knave then Riley is a knave.
Therefore, (1) Owen is a knight
(2) Riley is a knight
(3) Sofia is a knight
(4) Michael is a knight
(5) Grace is a knight
(6) Avery is a knight </think>
<answer> (1) Owen is a knight
(2) Riley is a knight
(3) Sofia is a knight
(4) Michael is a knight
(5) Grace is a knight
(6) Avery is a knight </answer>
Owen Riley Sofia Michael Grace Avery
(1) Owen is a knight
(2) Riley is a knight
(3) Sofia is a knight
(4) Michael is a knight
(5) Grace is a knight
(6) Avery is a knight
(('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 3), ('lying', 2)))
rule