
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
In a music competition, there are 360 participants. They are to be grouped in teams, with each team containing the same number of participants. The conditions are that there must be at least 12 teams and each team must have at least 20 participants. Determine the sum of all possible numbers of participants in each team.

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