
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
15 volleyball teams played a round-robin tournament, in which each team won exactly seven matches. How many triples of teams are there in this tournament where each team in the trio won one match against one of the other two teams?

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