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: Sofia, Scarlett, Mia, Aiden, and Grace. Sofia stated, "Mia is a knave or Aiden is a knight". "Sofia is a knight or Grace is a knave" - Scarlett. "Aiden is not a knight," Mia declared. Aiden told you that Scarlett is not a knight. "Mia is a knave and Mia is a knight," Grace claimed. 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 Sofia is a knight.  No contradiction is found in their claim that Mia is a knave or Aiden is a knight.
 Assume Mia is a knight.  No contradiction is found in their claim that Aiden is not a knight.
 Aiden cannot be a knight, because this would contradict the claim of Mia that Aiden is not a knight.
 Aiden cannot be a knave, because this would contradict the claim of Sofia that Mia is a knave or Aiden is a knight.
 We have exhausted all possibilities for Aiden, so let us go back and reconsider Mia.
 Assume Mia is a knave.  No contradiction is found in their false claim that Aiden is not a knight.
 Assume Aiden is a knight.  No contradiction is found in their claim that Scarlett is not a knight.
 Scarlett cannot be a knight, because this would contradict the claim of Aiden that Scarlett is not a knight.
 Scarlett cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Grace is a knave.
 We have exhausted all possibilities for Scarlett, so let us go back and reconsider Aiden.
 Aiden cannot be a knave, because this would contradict the false claim of Mia that Aiden is not a knight.
 We have exhausted all possibilities for Aiden and Mia, so let us go back and reconsider Sofia.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Mia is a knave or Aiden is a knight.
 Assume Mia is a knight.  No contradiction is found in their claim that Aiden is not a knight.
 Aiden cannot be a knight, because this would contradict the false claim of Sofia that Mia is a knave or Aiden is a knight.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Scarlett is not a knight.
 Assume Scarlett is a knight.  No contradiction is found in their claim that Sofia is a knight or Grace is a knave.
 Grace cannot be a knight, because this would contradict the claim of Scarlett that Sofia is a knight or Grace is a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Mia is a knave and Mia is a knight.
 Therefore, (1) Sofia is a knave
 (2) Scarlett is a knight
 (3) Mia is a knight
 (4) Aiden is a knave
 (5) Grace 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 5 inhabitants: Sofia, Scarlett, Mia, Aiden, and Grace. Sofia stated, "Mia is a knave or Aiden is a knight". "Sofia is a knight or Grace is a knave" - Scarlett. "Aiden is not a knight," Mia declared. Aiden told you that Scarlett is not a knight. "Mia is a knave and Mia is a knight," Grace claimed. 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 Sofia is a knight. No contradiction is found in their claim that Mia is a knave or Aiden is a knight.
Assume Mia is a knight. No contradiction is found in their claim that Aiden is not a knight.
Aiden cannot be a knight, because this would contradict the claim of Mia that Aiden is not a knight.
Aiden cannot be a knave, because this would contradict the claim of Sofia that Mia is a knave or Aiden is a knight.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Mia.
Assume Mia is a knave. No contradiction is found in their false claim that Aiden is not a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Scarlett is not a knight.
Scarlett cannot be a knight, because this would contradict the claim of Aiden that Scarlett is not a knight.
Scarlett cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Grace is a knave.
We have exhausted all possibilities for Scarlett, so let us go back and reconsider Aiden.
Aiden cannot be a knave, because this would contradict the false claim of Mia that Aiden is not a knight.
We have exhausted all possibilities for Aiden and Mia, so let us go back and reconsider Sofia.
Assume Sofia is a knave. No contradiction is found in their false claim that Mia is a knave or Aiden is a knight.
Assume Mia is a knight. No contradiction is found in their claim that Aiden is not a knight.
Aiden cannot be a knight, because this would contradict the false claim of Sofia that Mia is a knave or Aiden is a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that Scarlett is not a knight.
Assume Scarlett is a knight. No contradiction is found in their claim that Sofia is a knight or Grace is a knave.
Grace cannot be a knight, because this would contradict the claim of Scarlett that Sofia is a knight or Grace is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.
Therefore, (1) Sofia is a knave
(2) Scarlett is a knight
(3) Mia is a knight
(4) Aiden is a knave
(5) Grace is a knave </think>
<answer> (1) Sofia is a knave
(2) Scarlett is a knight
(3) Mia is a knight
(4) Aiden is a knave
(5) Grace is a knave </answer>
Sofia Scarlett Mia Aiden Grace
(1) Sofia is a knave
(2) Scarlett is a knight
(3) Mia is a knight
(4) Aiden is a knave
(5) Grace is a knave
(('or', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 4)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 2)))
rule