
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
On a tournament with  $ n \ge 3$  participants, every two participants played exactly one match and there were no draws. A three-element set of participants is called a *draw-triple* if they can be enumerated so that the ﬁrst defeated the second, the second defeated the third, and the third defeated the ﬁrst. Determine the largest possible number of draw-triples on such a tournament.

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