
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
If several people high-five each other in pairs (one person’s left hand high-fives another person’s right hand), and after each pair has high-fived once, it is found that each person's each hand has high-fived exactly 2021 times. How many groups of three people can be chosen from these people such that they can all high-five each other simultaneously?

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