
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 120 people sitting around a circular table - knights, who always tell the truth, and liars, who always lie. Each person made exactly one of the following two statements: 1) "My neighbor to the right is a knight"; 2) "The one who is two places to the right of me is a knight." How many liars could there be in total at the table?

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