
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 the diagram, three circles of radius 5 units intersect at the origin, and a square of side length 10 units (equal to the diameter of the circles) is placed such that its center is also at the origin. What is the number of square units in the area of just the overlapping region between the square and the circles but not including any region where the circles intersect each other? Express your answer in terms of $\pi$.

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