
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
There are a number of people who clap hands in pairs (one person's left hand claps with another person's right hand). After each pair claps hands once, it is found that each person's hand clapped exactly 2021 times. How many groups of three people can be chosen from these individuals such that each pair within the group can clap hands simultaneously?

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