
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
Several people played a single-round robin tournament in table tennis. At the end of the tournament, it turned out that for any four participants, there are two who scored the same number of points in the games among these four participants. What is the maximum number of tennis players who could have participated in this tournament? In table tennis, there are no draws, one point is awarded for a win, and zero points for a loss.

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