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