
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 round-robin tournament where every team plays every other team exactly once, each team wins 15 games and loses 15 games. Determine how many sets of three teams $\{A, B, C\}$ there are such that $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$.
A) 1135
B) 1200
C) 1240
D) 1270
E) 1305

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