
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

On an island, there are two tribes: knights and liars. Knights always tell the truth, and liars always lie. One day, 80 people sat at a round table, and each of them declared: "Among the 11 people sitting immediately after me in a clockwise direction, there are at least 9 liars." How many knights are sitting at the round table? Indicate all possible options.

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