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: Mia, Avery, Sebastian, Michael, William, Daniel, and Ava. Mia noted, "Avery is a knight or Sebastian is a knight". Avery said that Sebastian is a knight if and only if Avery is a knight. In Sebastian's words: "Mia is a knave or Avery is a knight". In a statement by Michael: "Avery is a knave or Mia is a knight". William remarked, "Sebastian is a knave and Avery is a knave". In a statement by Daniel: "If Mia is a knave then Mia is a knight". "If Sebastian is a knight then William is a knight," Ava 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 Mia is a knight.  No contradiction is found in their claim that Avery is a knight or Sebastian is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Sebastian is a knight if and only if Avery is a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Mia is a knave or Avery is a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that Avery is a knave or Mia is a knight.
 William cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Avery is a knave.
 Assume William is a knave.  No contradiction is found in their false claim that Sebastian is a knave and Avery is a knave.
 Assume Daniel is a knight.  No contradiction is found in their claim that If Mia is a knave then Mia is a knight.
 Ava cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knight then William is a knight.
 Assume Ava is a knave.  No contradiction is found in their false claim that If Sebastian is a knight then William is a knight.
 Therefore, (1) Mia is a knight
 (2) Avery is a knight
 (3) Sebastian is a knight
 (4) Michael is a knight
 (5) William is a knave
 (6) Daniel is a knight
 (7) Ava 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: Mia, Avery, Sebastian, Michael, William, Daniel, and Ava. Mia noted, "Avery is a knight or Sebastian is a knight". Avery said that Sebastian is a knight if and only if Avery is a knight. In Sebastian's words: "Mia is a knave or Avery is a knight". In a statement by Michael: "Avery is a knave or Mia is a knight". William remarked, "Sebastian is a knave and Avery is a knave". In a statement by Daniel: "If Mia is a knave then Mia is a knight". "If Sebastian is a knight then William is a knight," Ava 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 Mia is a knight. No contradiction is found in their claim that Avery is a knight or Sebastian is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Avery is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Mia is a knave or Avery is a knight.
Assume Michael is a knight. No contradiction is found in their claim that Avery is a knave or Mia is a knight.
William cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Avery is a knave.
Assume William is a knave. No contradiction is found in their false claim that Sebastian is a knave and Avery is a knave.
Assume Daniel is a knight. No contradiction is found in their claim that If Mia is a knave then Mia is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knight then William is a knight.
Assume Ava is a knave. No contradiction is found in their false claim that If Sebastian is a knight then William is a knight.
Therefore, (1) Mia is a knight
(2) Avery is a knight
(3) Sebastian is a knight
(4) Michael is a knight
(5) William is a knave
(6) Daniel is a knight
(7) Ava is a knave </think>
<answer> (1) Mia is a knight
(2) Avery is a knight
(3) Sebastian is a knight
(4) Michael is a knight
(5) William is a knave
(6) Daniel is a knight
(7) Ava is a knave </answer>
Mia Avery Sebastian Michael William Daniel Ava
(1) Mia is a knight
(2) Avery is a knight
(3) Sebastian is a knight
(4) Michael is a knight
(5) William is a knave
(6) Daniel is a knight
(7) Ava is a knave
(('or', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 4)))
rule