
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
A round-robin tournament is held where each of 25 teams played every other team exactly once. Every team won 12 games and lost 12 games; there were no ties. Determine how many sets of three teams $\{A, B, C\}$ exist where $A$ beat $B$, $B$ beat $C$, and $C$ beat $A$.
A) 500
B) 650
C) 800
D) 950
E) 1000

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