
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
Thirty people sit around a circular table. Each of them is either foolish or smart. Each person is asked: "Is your neighbor to the right smart or foolish?" A smart person always tells the truth, while a foolish person can either tell the truth or lie. It is known that the number of foolish people does not exceed $F$. For the largest possible value of $F$, can we always, knowing these answers, identify a smart person in this company?

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