
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 region shown is bounded by the arcs of circles having radius 6 units, where each arc subtends a central angle of 90 degrees at the center of its respective circle. These circles intersect at points of tangency. Calculate the area of this region. The area of the region can be expressed in the form \(a\sqrt{b} + c\pi\) square units, where \(\sqrt{b}\) is in its simplest form. Determine the value of \(a + b + c\).

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