
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
A $2022 \times 2022$ board is given. Maxim and Andrey take turns painting $2 \times 2$ squares on it with yellow and red colors along the cell edges, agreeing that each cell can be painted no more than once in yellow and no more than once in red. Cells first painted yellow and then red (or vice versa) become orange. Once all cells have been painted, the boys counted the number of orange cells. What are the possible numbers they could find?

Options for the answers:

○ $2022 \cdot 2022$

○ $2022 \cdot 2021$

○ $2021 \cdot 2020$

- $2022 \cdot 2020$

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