
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
Let \( n \) be a positive integer. There are \( 3n \) male and \( 3n \) female table tennis players. They are paired to form \( n \) male doubles teams, \( n \) female doubles teams, and \( n \) mixed doubles teams, with each player participating in only one event. What is the total number of ways to form these pairs?

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