
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 modified round-robin tournament with 27 teams, where each team played every other team exactly once, and every team won 13 games and lost 13 games, determine the number of sets of three teams {A, B, C} such that A beat B, B beat C, and C beat A.

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