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: Avery, Scarlett, Ava, Evelyn, James, Grace, and Isabella. According to Avery, "Isabella is a knight or Ava is a knave". Scarlett was heard saying, "If Ava is a knight then Evelyn is a knave". Ava noted, "Avery is not a knave". "Ava is a knight if and only if Isabella is a knave" - Evelyn. "If Grace is a knave then Ava is a knave," James mentioned. In a statement by Grace: "Evelyn is a knight". Isabella told you that If Evelyn is a knave then Isabella is 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 Avery is a knight.  No contradiction is found in their claim that Isabella is a knight or Ava is a knave.
 Assume Isabella is a knight.  No contradiction is found in their claim that If Evelyn is a knave then Isabella is a knight.
 Assume Evelyn is a knight.  No contradiction is found in their claim that Ava is a knight if and only if Isabella is a knave.
 Ava cannot be a knight, because this would contradict the claim of Evelyn that Ava is a knight if and only if Isabella is a knave.
 Ava cannot be a knave, because this would contradict the false claim of their own that Avery is not a knave.
 We have exhausted all possibilities for Ava, so let us go back and reconsider Evelyn.
 Assume Evelyn is a knave.  No contradiction is found in their false claim that Ava is a knight if and only if Isabella is a knave.
 Assume Ava is a knight.  No contradiction is found in their claim that Avery is not a knave.
 Assume Scarlett is a knight.  No contradiction is found in their claim that If Ava is a knight then Evelyn is a knave.
 Assume James is a knight.  No contradiction is found in their claim that If Grace is a knave then Ava is a knave.
 Grace cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.
 Grace cannot be a knave, because this would contradict the claim of James that If Grace is a knave then Ava is a knave.
 We have exhausted all possibilities for Grace, so let us go back and reconsider James.
 Assume James is a knave.  No contradiction is found in their false claim that If Grace is a knave then Ava is a knave.
 Grace cannot be a knight, because this would contradict the false claim of James that If Grace is a knave then Ava is a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Evelyn is a knight.
 Therefore, (1) Avery is a knight
 (2) Scarlett is a knight
 (3) Ava is a knight
 (4) Evelyn is a knave
 (5) James is a knave
 (6) Grace is a knave
 (7) Isabella 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: Avery, Scarlett, Ava, Evelyn, James, Grace, and Isabella. According to Avery, "Isabella is a knight or Ava is a knave". Scarlett was heard saying, "If Ava is a knight then Evelyn is a knave". Ava noted, "Avery is not a knave". "Ava is a knight if and only if Isabella is a knave" - Evelyn. "If Grace is a knave then Ava is a knave," James mentioned. In a statement by Grace: "Evelyn is a knight". Isabella told you that If Evelyn is a knave then Isabella is 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 Avery is a knight. No contradiction is found in their claim that Isabella is a knight or Ava is a knave.
Assume Isabella is a knight. No contradiction is found in their claim that If Evelyn is a knave then Isabella is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Ava is a knight if and only if Isabella is a knave.
Ava cannot be a knight, because this would contradict the claim of Evelyn that Ava is a knight if and only if Isabella is a knave.
Ava cannot be a knave, because this would contradict the false claim of their own that Avery is not a knave.
We have exhausted all possibilities for Ava, so let us go back and reconsider Evelyn.
Assume Evelyn is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Isabella is a knave.
Assume Ava is a knight. No contradiction is found in their claim that Avery is not a knave.
Assume Scarlett is a knight. No contradiction is found in their claim that If Ava is a knight then Evelyn is a knave.
Assume James is a knight. No contradiction is found in their claim that If Grace is a knave then Ava is a knave.
Grace cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.
Grace cannot be a knave, because this would contradict the claim of James that If Grace is a knave then Ava is a knave.
We have exhausted all possibilities for Grace, so let us go back and reconsider James.
Assume James is a knave. No contradiction is found in their false claim that If Grace is a knave then Ava is a knave.
Grace cannot be a knight, because this would contradict the false claim of James that If Grace is a knave then Ava is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Evelyn is a knight.
Therefore, (1) Avery is a knight
(2) Scarlett is a knight
(3) Ava is a knight
(4) Evelyn is a knave
(5) James is a knave
(6) Grace is a knave
(7) Isabella is a knight </think>
<answer> (1) Avery is a knight
(2) Scarlett is a knight
(3) Ava is a knight
(4) Evelyn is a knave
(5) James is a knave
(6) Grace is a knave
(7) Isabella is a knight </answer>
Avery Scarlett Ava Evelyn James Grace Isabella
(1) Avery is a knight
(2) Scarlett is a knight
(3) Ava is a knight
(4) Evelyn is a knave
(5) James is a knave
(6) Grace is a knave
(7) Isabella is a knight
(('or', ('telling-truth', 6), ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 3)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 6)), ('->', ('lying', 5), ('lying', 2)), ('telling-truth', 3), ('->', ('lying', 3), ('telling-truth', 6)))
rule