
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
Given that each team played every other team exactly once, with every team winning $15$ games and losing $6$ games, determine the total number of sets of four teams $\{A, B, C, D\}$ such that $A$ beat $B$, $B$ beat $C$, $C$ beat $D$, and $D$ beat $A$.

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