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: Harper, Mason, Riley, Samuel, Victoria, and Sebastian. According to Harper, "Riley is a knight if and only if Riley is a knave". In a statement by Mason: "Samuel is a knave if and only if Sebastian is a knight". In a statement by Riley: "Harper is a knave or Harper is a knight". "Sebastian is a knave or Mason is a knave," Samuel declared. In Victoria's words: "Riley is not a knave". Sebastian stated, "Riley is not 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
Harper cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.
 Assume Harper is a knave.  No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.
 Assume Riley is a knight.  No contradiction is found in their claim that Harper is a knave or Harper is a knight.
 Assume Mason is a knight.  No contradiction is found in their claim that Samuel is a knave if and only if Sebastian is a knight.
 Assume Samuel is a knight.  No contradiction is found in their claim that Sebastian is a knave or Mason is a knave.
 Sebastian cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave if and only if Sebastian is a knight.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Riley is not a knight.
 Assume Victoria is a knight.  No contradiction is found in their claim that Riley is not a knave.
 Therefore, (1) Harper is a knave
 (2) Mason is a knight
 (3) Riley is a knight
 (4) Samuel is a knight
 (5) Victoria is a knight
 (6) Sebastian 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 6 inhabitants: Harper, Mason, Riley, Samuel, Victoria, and Sebastian. According to Harper, "Riley is a knight if and only if Riley is a knave". In a statement by Mason: "Samuel is a knave if and only if Sebastian is a knight". In a statement by Riley: "Harper is a knave or Harper is a knight". "Sebastian is a knave or Mason is a knave," Samuel declared. In Victoria's words: "Riley is not a knave". Sebastian stated, "Riley is not 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> 
Harper cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.
Assume Harper is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.
Assume Riley is a knight. No contradiction is found in their claim that Harper is a knave or Harper is a knight.
Assume Mason is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Sebastian is a knight.
Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is a knave or Mason is a knave.
Sebastian cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave if and only if Sebastian is a knight.
Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is not a knight.
Assume Victoria is a knight. No contradiction is found in their claim that Riley is not a knave.
Therefore, (1) Harper is a knave
(2) Mason is a knight
(3) Riley is a knight
(4) Samuel is a knight
(5) Victoria is a knight
(6) Sebastian is a knave </think>
<answer> (1) Harper is a knave
(2) Mason is a knight
(3) Riley is a knight
(4) Samuel is a knight
(5) Victoria is a knight
(6) Sebastian is a knave </answer>
Harper Mason Riley Samuel Victoria Sebastian
(1) Harper is a knave
(2) Mason is a knight
(3) Riley is a knight
(4) Samuel is a knight
(5) Victoria is a knight
(6) Sebastian is a knave
(('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 5), ('lying', 1)), ('not', ('lying', 2)), ('not', ('telling-truth', 2)))
rule