
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
Six people, a mix of knights (who always tell the truth) and liars (who always lie), sat around a round table. Each of them was given a coin. Then, each person passed their coin to one of their two neighbors. After that, 3 people said, "I have one coin," and the other 3 said, "I have no coins." What is the maximum number of knights that could have been sitting at the table?

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