
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 and tell the truth to each other, while girls would lie to boys and tell the truth to each other. One of the children said to his right neighbor: "The majority of us are boys." The neighbor then said to his right neighbor: "The majority of us are girls," and he said to his right neighbor: "The majority of us are boys," and so on, until the last child said to the first one: "The majority of us are boys." How many boys were at the table?

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