
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
Each team has exactly three players and each player plays exactly once against each player from all the other teams. Determine the maximum number of teams that can enter the tournament given that a total of no more than 250 games can be played.

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