
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 sports league holds a round-robin tournament where every team plays every other team exactly once. Each of the teams wins $12$ games and loses $8$ games; there are no ties. 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) 385  
B) 462  
C) 665  
D) 868  
E) 945

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