
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
In each cell of a $1000 \times 1000$ square, a number is written such that in any rectangle with area $s$ whose sides are aligned along the cell boundaries and do not exceed the boundaries of the square, the sum of the numbers is the same. For which values of $s$ will the numbers in all cells necessarily be the same?

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