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: Samuel, Mason, Grace, David, and Zoey. Samuel asserted: "Zoey is not a knight". In a statement by Mason: "Zoey is a knave if and only if David is a knight". Grace expressed that Samuel is a knight. "Samuel is not a knave" - David. Zoey said that If David is a knight then Samuel 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 Samuel is a knight.  No contradiction is found in their claim that Zoey is not a knight.
 Zoey cannot be a knight, because this would contradict the claim of Samuel that Zoey is not a knight.
 Zoey cannot be a knave, because this would contradict the false claim of their own that If David is a knight then Samuel is a knight.
 We have exhausted all possibilities for Zoey, so let us go back and reconsider Samuel.
 Assume Samuel is a knave.  No contradiction is found in their false claim that Zoey is not a knight.
 Assume Zoey is a knight.  No contradiction is found in their claim that If David is a knight then Samuel is a knight.
 David cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.
 Assume David is a knave.  No contradiction is found in their false claim that Samuel is not a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that Zoey is a knave if and only if David is a knight.
 Grace cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.
 Assume Grace is a knave.  No contradiction is found in their false claim that Samuel is a knight.
 Therefore, (1) Samuel is a knave
 (2) Mason is a knight
 (3) Grace is a knave
 (4) David is a knave
 (5) Zoey 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 5 inhabitants: Samuel, Mason, Grace, David, and Zoey. Samuel asserted: "Zoey is not a knight". In a statement by Mason: "Zoey is a knave if and only if David is a knight". Grace expressed that Samuel is a knight. "Samuel is not a knave" - David. Zoey said that If David is a knight then Samuel 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 Samuel is a knight. No contradiction is found in their claim that Zoey is not a knight.
Zoey cannot be a knight, because this would contradict the claim of Samuel that Zoey is not a knight.
Zoey cannot be a knave, because this would contradict the false claim of their own that If David is a knight then Samuel is a knight.
We have exhausted all possibilities for Zoey, so let us go back and reconsider Samuel.
Assume Samuel is a knave. No contradiction is found in their false claim that Zoey is not a knight.
Assume Zoey is a knight. No contradiction is found in their claim that If David is a knight then Samuel is a knight.
David cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.
Assume David is a knave. No contradiction is found in their false claim that Samuel is not a knave.
Assume Mason is a knight. No contradiction is found in their claim that Zoey is a knave if and only if David is a knight.
Grace cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.
Assume Grace is a knave. No contradiction is found in their false claim that Samuel is a knight.
Therefore, (1) Samuel is a knave
(2) Mason is a knight
(3) Grace is a knave
(4) David is a knave
(5) Zoey is a knight </think>
<answer> (1) Samuel is a knave
(2) Mason is a knight
(3) Grace is a knave
(4) David is a knave
(5) Zoey is a knight </answer>
Samuel Mason Grace David Zoey
(1) Samuel is a knave
(2) Mason is a knight
(3) Grace is a knave
(4) David is a knave
(5) Zoey is a knight
(('not', ('telling-truth', 4)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('telling-truth', 0), ('not', ('lying', 0)), ('->', ('telling-truth', 3), ('telling-truth', 0)))
rule