
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
In a school chess tournament, boys and girls competed, with the number of boys being 5 times the number of girls. According to the tournament rules, each player played against every other player twice. How many players participated in total, given that the boys scored exactly twice as many points as the girls? (A win in a chess game counts as 1 point, a draw counts as 0.5 points, and a loss counts as 0 points.)

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