
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 teams are divided into 4 groups, with at least two teams in each group. Each group plays a round-robin tournament (every team in a group plays against every other team in that group exactly once), with a total of 66 matches played. How many teams participated in total? (List all possible numbers of participating teams)

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