
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 chess tournament, \( n \) women and \( 2n \) men participated. Everyone played exactly one game with each other. There were no draws, and the number of games won by the women is in the ratio of \( 7: 5 \) to the number of games won by the men. What is \( n \)?

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