
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 round table and agreed that boys would lie to girls but tell the truth to each other, and girls would lie to boys but tell the truth to each other. One of the children said to their right-hand neighbor, "The majority of us are boys." That neighbor said to their right-hand neighbor, "The majority of us are girls," and then that neighbor said to their right-hand neighbor, "The majority of us are boys," and so on, continuing until the last child said to the first, "The majority of us are boys." How many boys were seated at the table?

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