
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
An equilateral triangle with side length 16 cm is inscribed in a circle. A side of the triangle is the diameter of another circle. Calculate the sum of the areas of two small shaded regions in square centimeters in simplest radical form and express it as $a\pi - b\sqrt{c}$. Find $a+b+c$.

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