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: Victoria, Samuel, Aiden, Joseph, Riley, Alexander, and Zoey. "If Alexander is a knave then Zoey is a knight," Victoria claimed. As Samuel put it, "Aiden is a knave if and only if Riley is a knight". "If Zoey is a knave then Riley is a knave," Aiden claimed. Joseph noted, "Zoey is a knave". Riley stated, "Alexander is not a knave". Alexander told you that Riley is a knave or Alexander is a knight. According to Zoey, "Alexander 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
Assume Victoria is a knight.  No contradiction is found in their claim that If Alexander is a knave then Zoey is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Riley is a knave or Alexander is a knight.
 Assume Riley is a knight.  No contradiction is found in their claim that Alexander is not a knave.
 Zoey cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Alexander is not a knight.
 Assume Samuel is a knight.  No contradiction is found in their claim that Aiden is a knave if and only if Riley is a knight.
 Aiden cannot be a knight, because this would contradict the claim of Samuel that Aiden is a knave if and only if Riley is a knight.
 Assume Aiden is a knave.  No contradiction is found in their false claim that If Zoey is a knave then Riley is a knave.
 Assume Joseph is a knight.  No contradiction is found in their claim that Zoey is a knave.
 Therefore, (1) Victoria is a knight
 (2) Samuel is a knight
 (3) Aiden is a knave
 (4) Joseph is a knight
 (5) Riley is a knight
 (6) Alexander is a knight
 (7) Zoey 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 7 inhabitants: Victoria, Samuel, Aiden, Joseph, Riley, Alexander, and Zoey. "If Alexander is a knave then Zoey is a knight," Victoria claimed. As Samuel put it, "Aiden is a knave if and only if Riley is a knight". "If Zoey is a knave then Riley is a knave," Aiden claimed. Joseph noted, "Zoey is a knave". Riley stated, "Alexander is not a knave". Alexander told you that Riley is a knave or Alexander is a knight. According to Zoey, "Alexander 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> 
Assume Victoria is a knight. No contradiction is found in their claim that If Alexander is a knave then Zoey is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Riley is a knave or Alexander is a knight.
Assume Riley is a knight. No contradiction is found in their claim that Alexander is not a knave.
Zoey cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Alexander is not a knight.
Assume Samuel is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Riley is a knight.
Aiden cannot be a knight, because this would contradict the claim of Samuel that Aiden is a knave if and only if Riley is a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that If Zoey is a knave then Riley is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Zoey is a knave.
Therefore, (1) Victoria is a knight
(2) Samuel is a knight
(3) Aiden is a knave
(4) Joseph is a knight
(5) Riley is a knight
(6) Alexander is a knight
(7) Zoey is a knave </think>
<answer> (1) Victoria is a knight
(2) Samuel is a knight
(3) Aiden is a knave
(4) Joseph is a knight
(5) Riley is a knight
(6) Alexander is a knight
(7) Zoey is a knave </answer>
Victoria Samuel Aiden Joseph Riley Alexander Zoey
(1) Victoria is a knight
(2) Samuel is a knight
(3) Aiden is a knave
(4) Joseph is a knight
(5) Riley is a knight
(6) Alexander is a knight
(7) Zoey is a knave
(('->', ('lying', 5), ('telling-truth', 6)), ('<=>', ('lying', 2), ('telling-truth', 4)), ('->', ('lying', 6), ('lying', 4)), ('lying', 6), ('not', ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 5)), ('not', ('telling-truth', 5)))
rule