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: Alexander, Aria, Grace, Aurora, Scarlett, Sofia, and Mason. Alexander said, "Grace is a knave or Scarlett is a knave." According to Aria, "Mason is a knight". "Aurora is a knave," Grace declared. "Grace is a knight and Sofia is a knight," Aurora mentioned. Scarlett said, "Scarlett is a knight or Mason is a knave." Sofia asserted: "Grace is a knight and Scarlett is a knight". Mason said, "Grace is not 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 Alexander is a knight.  No contradiction is found in their claim that Grace is a knave or Scarlett is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Aurora is a knave.
 Aurora cannot be a knight, because this would contradict the claim of Grace that Aurora is a knave.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Grace is a knight and Sofia is a knight.
 Sofia cannot be a knight, because this would contradict the false claim of Aurora that Grace is a knight and Sofia is a knight.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Grace is a knight and Scarlett is a knight.
 Scarlett cannot be a knight, because this would contradict the claim of Alexander that Grace is a knave or Scarlett is a knave.
 Assume Scarlett is a knave.  No contradiction is found in their false claim that Scarlett is a knight or Mason is a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that Grace is not a knave.
 Assume Aria is a knight.  No contradiction is found in their claim that Mason is a knight.
 Therefore, (1) Alexander is a knight
 (2) Aria is a knight
 (3) Grace is a knight
 (4) Aurora is a knave
 (5) Scarlett is a knave
 (6) Sofia is a knave
 (7) Mason 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 7 inhabitants: Alexander, Aria, Grace, Aurora, Scarlett, Sofia, and Mason. Alexander said, "Grace is a knave or Scarlett is a knave." According to Aria, "Mason is a knight". "Aurora is a knave," Grace declared. "Grace is a knight and Sofia is a knight," Aurora mentioned. Scarlett said, "Scarlett is a knight or Mason is a knave." Sofia asserted: "Grace is a knight and Scarlett is a knight". Mason said, "Grace is not 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 Alexander is a knight. No contradiction is found in their claim that Grace is a knave or Scarlett is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Aurora is a knave.
Aurora cannot be a knight, because this would contradict the claim of Grace that Aurora is a knave.
Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knight and Sofia is a knight.
Sofia cannot be a knight, because this would contradict the false claim of Aurora that Grace is a knight and Sofia is a knight.
Assume Sofia is a knave. No contradiction is found in their false claim that Grace is a knight and Scarlett is a knight.
Scarlett cannot be a knight, because this would contradict the claim of Alexander that Grace is a knave or Scarlett is a knave.
Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight or Mason is a knave.
Assume Mason is a knight. No contradiction is found in their claim that Grace is not a knave.
Assume Aria is a knight. No contradiction is found in their claim that Mason is a knight.
Therefore, (1) Alexander is a knight
(2) Aria is a knight
(3) Grace is a knight
(4) Aurora is a knave
(5) Scarlett is a knave
(6) Sofia is a knave
(7) Mason is a knight </think>
<answer> (1) Alexander is a knight
(2) Aria is a knight
(3) Grace is a knight
(4) Aurora is a knave
(5) Scarlett is a knave
(6) Sofia is a knave
(7) Mason is a knight </answer>
Alexander Aria Grace Aurora Scarlett Sofia Mason
(1) Alexander is a knight
(2) Aria is a knight
(3) Grace is a knight
(4) Aurora is a knave
(5) Scarlett is a knave
(6) Sofia is a knave
(7) Mason is a knight
(('or', ('lying', 2), ('lying', 4)), ('telling-truth', 6), ('lying', 3), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('lying', 6)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('lying', 2)))
rule