
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
13 children sat around a circular table and agreed that boys would lie to girls but tell the truth to each other, while girls would lie to boys but tell the truth to each other. One of the children told his right-hand neighbor, "Most of us are boys." The neighbor then told his right-hand neighbor, "Most of us are girls." This pattern continued in the same way, alternating statements, until the last child told the first, "Most of us are boys." How many boys are at the table?

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