
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
Four circles of radius 5 units intersect at the origin. What is the number of square units in the area of the shaded region, where the shaded regions are defined as differences between specific circular sections and square areas tangent to circle segments? (Include a conceptual diagram similar to the original problem, but adapt it to account for the new radius 5 and use squares for subtracted areas).

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