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 7 inhabitants: Jacob, Aria, Owen, Avery, Michael, Samuel, and Grace. Jacob noted, "Grace is a knave if and only if Avery is a knave". Aria remarked, "Grace is a knave". "Michael is a knave if and only if Michael is a knight" - Owen. According to Avery, "Jacob is a knight". Michael was heard saying, "Jacob is a knave if and only if Grace is a knight". "Avery is a knight," Samuel mentioned. "Michael is a knight if and only if Owen is a knight," Grace claimed. 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 Jacob is a knight.  No contradiction is found in their claim that Grace is a knave if and only if Avery is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Michael is a knight if and only if Owen is a knight.
 Michael cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Grace is a knight.
 Assume Michael is a knave.  No contradiction is found in their false claim that Jacob is a knave if and only if Grace is a knight.
 Owen cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Michael is a knight.
 Assume Owen is a knave.  No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Jacob is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Grace is a knave.
 Assume Aria is a knave.  No contradiction is found in their false claim that Grace is a knave.
 Assume Samuel is a knight.  No contradiction is found in their claim that Avery is a knight.
 Therefore, (1) Jacob is a knight
 (2) Aria is a knave
 (3) Owen is a knave
 (4) Avery is a knight
 (5) Michael is a knave
 (6) Samuel is a knight
 (7) Grace 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 7 inhabitants: Jacob, Aria, Owen, Avery, Michael, Samuel, and Grace. Jacob noted, "Grace is a knave if and only if Avery is a knave". Aria remarked, "Grace is a knave". "Michael is a knave if and only if Michael is a knight" - Owen. According to Avery, "Jacob is a knight". Michael was heard saying, "Jacob is a knave if and only if Grace is a knight". "Avery is a knight," Samuel mentioned. "Michael is a knight if and only if Owen is a knight," Grace claimed. 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 Jacob is a knight. No contradiction is found in their claim that Grace is a knave if and only if Avery is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Michael is a knight if and only if Owen is a knight.
Michael cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Grace is a knight.
Assume Michael is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Grace is a knight.
Owen cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Michael is a knight.
Assume Owen is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Jacob is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Grace is a knave.
Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knave.
Assume Samuel is a knight. No contradiction is found in their claim that Avery is a knight.
Therefore, (1) Jacob is a knight
(2) Aria is a knave
(3) Owen is a knave
(4) Avery is a knight
(5) Michael is a knave
(6) Samuel is a knight
(7) Grace is a knight </think>
<answer> (1) Jacob is a knight
(2) Aria is a knave
(3) Owen is a knave
(4) Avery is a knight
(5) Michael is a knave
(6) Samuel is a knight
(7) Grace is a knight </answer>
Jacob Aria Owen Avery Michael Samuel Grace
(1) Jacob is a knight
(2) Aria is a knave
(3) Owen is a knave
(4) Avery is a knight
(5) Michael is a knave
(6) Samuel is a knight
(7) Grace is a knight
(('<=>', ('lying', 6), ('lying', 3)), ('lying', 6), ('<=>', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 0), ('<=>', ('lying', 0), ('telling-truth', 6)), ('telling-truth', 3), ('<=>', ('telling-truth', 4), ('telling-truth', 2)))
rule