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, Avery, Riley, Chloe, Jack, Emily, and Jacob. Alexander asserted: "If Avery is a knight then Jacob is a knight". Avery asserted: "Emily is a knight and Avery is a knight". Riley expressed that Avery is a knave and Emily is a knight. Chloe noted, "Avery is not a knave". Jack was heard saying, "Jacob is not a knave". Emily remarked, "Chloe is a knight if and only if Chloe is a knave". Jacob commented, "Alexander is a knight or Jack 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 Alexander is a knight.  No contradiction is found in their claim that If Avery is a knight then Jacob is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Emily is a knight and Avery is a knight.
 Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.
 Emily cannot be a knave, because this would contradict the claim of Avery that Emily is a knight and Avery is a knight.
 We have exhausted all possibilities for Emily, so let us go back and reconsider Avery.
 Assume Avery is a knave.  No contradiction is found in their false claim that Emily is a knight and Avery is a knight.
 Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.
 Assume Emily is a knave.  No contradiction is found in their false claim that Chloe is a knight if and only if Chloe is a knave.
 Chloe cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.
 Assume Chloe is a knave.  No contradiction is found in their false claim that Avery is not a knave.
 Assume Jacob is a knight.  No contradiction is found in their claim that Alexander is a knight or Jack is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that Jacob is not a knave.
 Riley cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Emily is a knight.
 Assume Riley is a knave.  No contradiction is found in their false claim that Avery is a knave and Emily is a knight.
 Therefore, (1) Alexander is a knight
 (2) Avery is a knave
 (3) Riley is a knave
 (4) Chloe is a knave
 (5) Jack is a knight
 (6) Emily is a knave
 (7) Jacob 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, Avery, Riley, Chloe, Jack, Emily, and Jacob. Alexander asserted: "If Avery is a knight then Jacob is a knight". Avery asserted: "Emily is a knight and Avery is a knight". Riley expressed that Avery is a knave and Emily is a knight. Chloe noted, "Avery is not a knave". Jack was heard saying, "Jacob is not a knave". Emily remarked, "Chloe is a knight if and only if Chloe is a knave". Jacob commented, "Alexander is a knight or Jack 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 Alexander is a knight. No contradiction is found in their claim that If Avery is a knight then Jacob is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Emily is a knight and Avery is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.
Emily cannot be a knave, because this would contradict the claim of Avery that Emily is a knight and Avery is a knight.
We have exhausted all possibilities for Emily, so let us go back and reconsider Avery.
Assume Avery is a knave. No contradiction is found in their false claim that Emily is a knight and Avery is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knight if and only if Chloe is a knave.
Assume Emily is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Chloe is a knave.
Chloe cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.
Assume Chloe is a knave. No contradiction is found in their false claim that Avery is not a knave.
Assume Jacob is a knight. No contradiction is found in their claim that Alexander is a knight or Jack is a knight.
Assume Jack is a knight. No contradiction is found in their claim that Jacob is not a knave.
Riley cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Emily is a knight.
Assume Riley is a knave. No contradiction is found in their false claim that Avery is a knave and Emily is a knight.
Therefore, (1) Alexander is a knight
(2) Avery is a knave
(3) Riley is a knave
(4) Chloe is a knave
(5) Jack is a knight
(6) Emily is a knave
(7) Jacob is a knight </think>
<answer> (1) Alexander is a knight
(2) Avery is a knave
(3) Riley is a knave
(4) Chloe is a knave
(5) Jack is a knight
(6) Emily is a knave
(7) Jacob is a knight </answer>
Alexander Avery Riley Chloe Jack Emily Jacob
(1) Alexander is a knight
(2) Avery is a knave
(3) Riley is a knave
(4) Chloe is a knave
(5) Jack is a knight
(6) Emily is a knave
(7) Jacob is a knight
(('->', ('telling-truth', 1), ('telling-truth', 6)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('lying', 1), ('telling-truth', 5)), ('not', ('lying', 1)), ('not', ('lying', 6)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('or', ('telling-truth', 0), ('telling-truth', 4)))
rule