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: Riley, Samuel, Grace, Abigail, Harper, and Aria. Riley remarked, "Samuel is a knave or Abigail is a knight". As Samuel put it, "Harper is a knave or Grace is a knight". As Grace put it, "Harper is a knave and Aria is a knight". Abigail asserted: "Riley is a knight". As Harper put it, "Abigail is a knight and Grace is a knight". In a statement by Aria: "Riley is not a knave". 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 Riley is a knight.  No contradiction is found in their claim that Samuel is a knave or Abigail is a knight.
 Assume Samuel is a knight.  No contradiction is found in their claim that Harper is a knave or Grace is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Abigail is a knight and Grace is a knight.
 Assume Abigail is a knight.  No contradiction is found in their claim that Riley is a knight.
 Grace cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Aria is a knight.
 Grace cannot be a knave, because this would contradict the claim of Samuel that Harper is a knave or Grace is a knight.
 We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.
 Abigail cannot be a knave, because this would contradict the claim of Riley that Samuel is a knave or Abigail is a knight.
 We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
 Assume Harper is a knave.  No contradiction is found in their false claim that Abigail is a knight and Grace is a knight.
 Assume Abigail is a knight.  No contradiction is found in their claim that Riley is a knight.
 Grace cannot be a knight, because this would contradict the false claim of Harper that Abigail is a knight and Grace is a knight.
 Assume Grace is a knave.  No contradiction is found in their false claim that Harper is a knave and Aria is a knight.
 Aria cannot be a knight, because this would contradict the false claim of Grace that Harper is a knave and Aria is a knight.
 Aria cannot be a knave, because this would contradict the false claim of their own that Riley is not a knave.
 We have exhausted all possibilities for Aria and Grace, so let us go back and reconsider Abigail.
 Abigail cannot be a knave, because this would contradict the claim of Riley that Samuel is a knave or Abigail is a knight.
 We have exhausted all possibilities for Abigail and Harper, so let us go back and reconsider Samuel.
 Assume Samuel is a knave.  No contradiction is found in their false claim that Harper is a knave or Grace is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Abigail is a knight and Grace is a knight.
 Assume Abigail is a knight.  No contradiction is found in their claim that Riley is a knight.
 Grace cannot be a knight, because this would contradict the false claim of Samuel that Harper is a knave or Grace is a knight.
 Grace cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Grace is a knight.
 We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.
 Abigail cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.
 We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
 Harper cannot be a knave, because this would contradict the false claim of Samuel that Harper is a knave or Grace is a knight.
 We have exhausted all possibilities for Harper and Samuel, so let us go back and reconsider Riley.
 Assume Riley is a knave.  No contradiction is found in their false claim that Samuel is a knave or Abigail is a knight.
 Assume Samuel is a knight.  No contradiction is found in their claim that Harper is a knave or Grace is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Abigail is a knight and Grace is a knight.
 Abigail cannot be a knight, because this would contradict the false claim of Riley that Samuel is a knave or Abigail is a knight.
 Abigail cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Grace is a knight.
 We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
 Assume Harper is a knave.  No contradiction is found in their false claim that Abigail is a knight and Grace is a knight.
 Abigail cannot be a knight, because this would contradict the false claim of Riley that Samuel is a knave or Abigail is a knight.
 Assume Abigail is a knave.  No contradiction is found in their false claim that Riley is a knight.
 Assume Grace is a knight.  No contradiction is found in their claim that Harper is a knave and Aria is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.
 Aria cannot be a knave, because this would contradict the claim of Grace that Harper is a knave and Aria is a knight.
 We have exhausted all possibilities for Aria, so let us go back and reconsider Grace.
 Assume Grace is a knave.  No contradiction is found in their false claim that Harper is a knave and Aria is a knight.
 Aria cannot be a knight, because this would contradict the false claim of Grace that Harper is a knave and Aria is a knight.
 Assume Aria is a knave.  No contradiction is found in their false claim that Riley is not a knave.
 Therefore, (1) Riley is a knave
 (2) Samuel is a knight
 (3) Grace is a knave
 (4) Abigail is a knave
 (5) Harper is a knave
 (6) Aria 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 6 inhabitants: Riley, Samuel, Grace, Abigail, Harper, and Aria. Riley remarked, "Samuel is a knave or Abigail is a knight". As Samuel put it, "Harper is a knave or Grace is a knight". As Grace put it, "Harper is a knave and Aria is a knight". Abigail asserted: "Riley is a knight". As Harper put it, "Abigail is a knight and Grace is a knight". In a statement by Aria: "Riley is not a knave". 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 Riley is a knight. No contradiction is found in their claim that Samuel is a knave or Abigail is a knight.
Assume Samuel is a knight. No contradiction is found in their claim that Harper is a knave or Grace is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Grace is a knight.
Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight.
Grace cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Aria is a knight.
Grace cannot be a knave, because this would contradict the claim of Samuel that Harper is a knave or Grace is a knight.
We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.
Abigail cannot be a knave, because this would contradict the claim of Riley that Samuel is a knave or Abigail is a knight.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knight and Grace is a knight.
Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight.
Grace cannot be a knight, because this would contradict the false claim of Harper that Abigail is a knight and Grace is a knight.
Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knave and Aria is a knight.
Aria cannot be a knight, because this would contradict the false claim of Grace that Harper is a knave and Aria is a knight.
Aria cannot be a knave, because this would contradict the false claim of their own that Riley is not a knave.
We have exhausted all possibilities for Aria and Grace, so let us go back and reconsider Abigail.
Abigail cannot be a knave, because this would contradict the claim of Riley that Samuel is a knave or Abigail is a knight.
We have exhausted all possibilities for Abigail and Harper, so let us go back and reconsider Samuel.
Assume Samuel is a knave. No contradiction is found in their false claim that Harper is a knave or Grace is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Grace is a knight.
Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight.
Grace cannot be a knight, because this would contradict the false claim of Samuel that Harper is a knave or Grace is a knight.
Grace cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Grace is a knight.
We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.
Abigail cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
Harper cannot be a knave, because this would contradict the false claim of Samuel that Harper is a knave or Grace is a knight.
We have exhausted all possibilities for Harper and Samuel, so let us go back and reconsider Riley.
Assume Riley is a knave. No contradiction is found in their false claim that Samuel is a knave or Abigail is a knight.
Assume Samuel is a knight. No contradiction is found in their claim that Harper is a knave or Grace is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Grace is a knight.
Abigail cannot be a knight, because this would contradict the false claim of Riley that Samuel is a knave or Abigail is a knight.
Abigail cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Grace is a knight.
We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knight and Grace is a knight.
Abigail cannot be a knight, because this would contradict the false claim of Riley that Samuel is a knave or Abigail is a knight.
Assume Abigail is a knave. No contradiction is found in their false claim that Riley is a knight.
Assume Grace is a knight. No contradiction is found in their claim that Harper is a knave and Aria is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.
Aria cannot be a knave, because this would contradict the claim of Grace that Harper is a knave and Aria is a knight.
We have exhausted all possibilities for Aria, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knave and Aria is a knight.
Aria cannot be a knight, because this would contradict the false claim of Grace that Harper is a knave and Aria is a knight.
Assume Aria is a knave. No contradiction is found in their false claim that Riley is not a knave.
Therefore, (1) Riley is a knave
(2) Samuel is a knight
(3) Grace is a knave
(4) Abigail is a knave
(5) Harper is a knave
(6) Aria is a knave </think>
<answer> (1) Riley is a knave
(2) Samuel is a knight
(3) Grace is a knave
(4) Abigail is a knave
(5) Harper is a knave
(6) Aria is a knave </answer>
Riley Samuel Grace Abigail Harper Aria
(1) Riley is a knave
(2) Samuel is a knight
(3) Grace is a knave
(4) Abigail is a knave
(5) Harper is a knave
(6) Aria is a knave
(('or', ('lying', 1), ('telling-truth', 3)), ('or', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 4), ('telling-truth', 5)), ('telling-truth', 0), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 0)))
rule