
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, five circles of radius 5 units intersect at the origin. Calculate the number of square units in the area of the shaded region, which is structured similarly to the original problem but includes an additional circle. Express your answer in terms of $\pi$. Assume each shaded sector is similarly formed by the intersection of quarter circles and triangles like the original setup.

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