
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, 23 teams participated. Each team played exactly one match with every other team. We say that 3 teams form a "cycle of victories" if, considering only the matches between them, each team won exactly once. What is the maximum number of such cycles that could have occurred during the tournament?

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