
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
There are 10 people sitting around a round table, some of whom are knights and the rest are liars (knights always tell the truth, and liars always lie). It is known that among them there is at least one knight and at least one liar. What is the maximum number of people sitting at the table that can say: "Both of my neighbors are knights"? (A statement is considered false if it is even partially untrue.)

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