
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 a \(5 \times 5\) square, some cells are painted black as shown in the picture. Consider all possible squares whose sides align with the grid lines. How many of these squares have an equal number of black and white cells?

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