
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. The outcome of each tennis match is a win for one player and a loss for the other players; there are no ties. Suppose that whenever  $A$  and  $B$  are players in the tournament for which  $A$  won (strictly) more matches than  $B$  over the course of the tournament, it is also the case that  $A$  won the match against  $B$  during the tournament. In how many ways could the tournament have gone?

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