
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
The diagram is comprised of three intersecting circles each with a radius of 5 units. Each circle has a central angle of 90 degrees and intersects at points of tangency. Calculate the area of the region enclosed by these arcs. Express the area in the form \(a\sqrt{b} + c\pi\) square units, where \(\sqrt{b}\) is a radical in simplest form. Find the value of \(a + b + c\).

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