
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 is a sequence of numbers from 1 to 2021 written on a board. Denis wants to choose 1010 of these numbers such that the sum of any two of the chosen numbers is neither 2021 nor 2022. How many ways are there to do this?

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