
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 with a radius of 6 units, each having a central angle measure of 30 degrees, and intersecting at points of tangency. Additionally, there is a smaller circle of radius 3 units at the center, touching all the arcs at their points closest to the center. Calculate the area of the region outside the smaller circle but inside the arcs. The area of the region can be expressed in the form \(a\sqrt{b} + c\pi\) square units, where \(\sqrt{b}\) is a radical in simplest form. What is the value of \(a + b + c\)?

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