
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
2n (n > 5) people—knights and liars—are sitting around a round table. Liars always give false answers to any question, while knights always tell the truth. Each person knows who is a knight and who is a liar. Each of them answered two questions: "Who is your neighbor on the left?" and "Who is your neighbor on the right?" A sage, who knows that there are liars at the table but fewer than knights, was given the number of "Knight" and "Liar" responses and correctly determined the number of knights. How many "Knight" responses did the sage receive? Explain your answer.

Present the answer in LaTex format: \boxed{Your answer}
user