
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

Six distinguishable players are participating in a tennis tournament. Each player plays one match of tennis against every other player. There are no ties in this tournament—each tennis match results in a win for one player and a loss for the other. Suppose that whenever \( A \) and \( B \) are players in the tournament such that \( A \) wins strictly more matches than \( B \) over the course of the tournament, it is also true that \( A \) wins the match against \( B \) in the tournament. In how many ways could the tournament have gone?

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