
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, every team plays every other team exactly once. Each team won $8$ games and lost all other games; there were no ties. Determine how many sets of four teams \(\{A, B, C, D\}\) exist such that \(A\) beat \(B\), \(B\) beat \(C\), \(C\) beat \(D\), and \(D\) beat \(A\).
A) 504
B) 630
C) 756
D) 882
E) 1008

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