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 5 inhabitants: Sofia, Jack, Grace, Jacob, and Jackson. Sofia told you that Jackson is a knave and Grace is a knave. Jack expressed that Sofia is a knave and Jacob is a knight. Grace remarked, "Jackson is a knave if and only if Jack is a knight". "Sofia is a knave or Jack is a knave," Jacob declared. "Grace is a knave and Jack is a knave" - Jackson. 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 Sofia is a knight.  No contradiction is found in their claim that Jackson is a knave and Grace is a knave.
 Jackson cannot be a knight, because this would contradict the claim of Sofia that Jackson is a knave and Grace is a knave.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Grace is a knave and Jack is a knave.
 Grace cannot be a knight, because this would contradict the claim of Sofia that Jackson is a knave and Grace is a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Jackson is a knave if and only if Jack is a knight.
 Jack cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Jacob is a knight.
 Jack cannot be a knave, because this would contradict the false claim of Jackson that Grace is a knave and Jack is a knave.
 We have exhausted all possibilities for Jack, Grace, and Jackson, so let us go back and reconsider Sofia.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Jackson is a knave and Grace is a knave.
 Assume Jackson is a knight.  No contradiction is found in their claim that Grace is a knave and Jack is a knave.
 Grace cannot be a knight, because this would contradict the claim of Jackson that Grace is a knave and Jack is a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Jackson is a knave if and only if Jack is a knight.
 Jack cannot be a knight, because this would contradict the claim of Jackson that Grace is a knave and Jack is a knave.
 Jack cannot be a knave, because this would contradict the false claim of Grace that Jackson is a knave if and only if Jack is a knight.
 We have exhausted all possibilities for Jack and Grace, so let us go back and reconsider Jackson.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Grace is a knave and Jack is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Jackson is a knave if and only if Jack is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that Sofia is a knave and Jacob is a knight.
 Assume Jacob is a knight.  No contradiction is found in their claim that Sofia is a knave or Jack is a knave.
 Therefore, (1) Sofia is a knave
 (2) Jack is a knight
 (3) Grace is a knight
 (4) Jacob is a knight
 (5) Jackson 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 5 inhabitants: Sofia, Jack, Grace, Jacob, and Jackson. Sofia told you that Jackson is a knave and Grace is a knave. Jack expressed that Sofia is a knave and Jacob is a knight. Grace remarked, "Jackson is a knave if and only if Jack is a knight". "Sofia is a knave or Jack is a knave," Jacob declared. "Grace is a knave and Jack is a knave" - Jackson. 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 Sofia is a knight. No contradiction is found in their claim that Jackson is a knave and Grace is a knave.
Jackson cannot be a knight, because this would contradict the claim of Sofia that Jackson is a knave and Grace is a knave.
Assume Jackson is a knave. No contradiction is found in their false claim that Grace is a knave and Jack is a knave.
Grace cannot be a knight, because this would contradict the claim of Sofia that Jackson is a knave and Grace is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Jacob is a knight.
Jack cannot be a knave, because this would contradict the false claim of Jackson that Grace is a knave and Jack is a knave.
We have exhausted all possibilities for Jack, Grace, and Jackson, so let us go back and reconsider Sofia.
Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is a knave and Grace is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that Grace is a knave and Jack is a knave.
Grace cannot be a knight, because this would contradict the claim of Jackson that Grace is a knave and Jack is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of Jackson that Grace is a knave and Jack is a knave.
Jack cannot be a knave, because this would contradict the false claim of Grace that Jackson is a knave if and only if Jack is a knight.
We have exhausted all possibilities for Jack and Grace, so let us go back and reconsider Jackson.
Assume Jackson is a knave. No contradiction is found in their false claim that Grace is a knave and Jack is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Jack is a knight.
Assume Jack is a knight. No contradiction is found in their claim that Sofia is a knave and Jacob is a knight.
Assume Jacob is a knight. No contradiction is found in their claim that Sofia is a knave or Jack is a knave.
Therefore, (1) Sofia is a knave
(2) Jack is a knight
(3) Grace is a knight
(4) Jacob is a knight
(5) Jackson is a knave </think>
<answer> (1) Sofia is a knave
(2) Jack is a knight
(3) Grace is a knight
(4) Jacob is a knight
(5) Jackson is a knave </answer>
Sofia Jack Grace Jacob Jackson
(1) Sofia is a knave
(2) Jack is a knight
(3) Grace is a knight
(4) Jacob is a knight
(5) Jackson is a knave
(('and', ('lying', 4), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 1)), ('and', ('lying', 2), ('lying', 1)))
rule