
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 isosceles triangle ABC, where AB = AC = 16 cm and BC is the diameter of the circle with center O. The apex angle BAC is 120 degrees. Two smaller shaded regions are formed by drawing the circle. Determine the area of these shaded regions in the form $a\pi - b\sqrt{c}$. Find the value of $a+b+c$.

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