
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
19 table tennis players are divided into three teams, with each team having a certain number of players. They will play singles matches where players from the same team do not compete against each other, but players from different teams will compete against each other in matches. The maximum number of matches that can be played is ____ matches.

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