
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]


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In a football championship, 20 teams participate, each playing once against every other team. What is the minimum number of games that must be played so that among any three teams, there are at least two teams that have already played against each other?

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