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