
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
Petya wrote ones in 16 cells of a \(5 \times 5\) square and zeros in the remaining nine cells. Petya then found all possible sums in the four cells forming a \(2 \times 2\) square. It turned out that the sum of the sixteen sums found by Petya was 28. In which cells are the ones written? All options should be specified.

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