
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 triangle shown is an equilateral triangle with side length 16 cm. A side of the triangle is the diameter of the circle, and another circle is inscribed within the equilateral triangle. If the sum of the areas of the two small shaded regions (between the inscribed circle and the central circle) in square centimeters is in simplest radical form $a\pi - b\sqrt{c}$, find $a+b+c$.**

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