
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 board of size \(2022 \times 2022\) is given. Egor and Matvey take turns coloring \(2 \times 2\) squares along the lines of the grid with red and yellow colors. They agreed that each cell can be painted no more than once in red and no more than once in yellow. Cells painted yellow first and then red (or vice versa) turn orange. Once all cells have been painted, the boys count how many of them are orange. What outcomes could they have obtained?

Possible answers:

○ \(2022 \cdot 2021\)

○ \(2022 \cdot 2020\)

○ \(2021 \cdot 2020\)

○ \(2022 \cdot 2022\)


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