
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
Consider a scenario where two rectangles with integer dimensions have a perimeter of 100 cm. One rectangle is aligned with the axes, while the second rectangle is rotated by 45 degrees, fitting within the perimeter limit. What is the greatest possible difference between the areas of these two rectangles?

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