
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 diagram, four circles of radius 5 units intersect at the origin. What is the number of square units in the area of the shaded region that forms within each intersection? Each shaded region is now shaped as a sector. Express your answer in terms of $\pi$.

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