
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
We consider a white \(5 \times 5\) square consisting of 25 unit squares. How many different ways are there to paint one or more of the unit squares black so that the resulting black area forms a rectangle?

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