
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 10 cm is inscribed in a circle. Two of the vertices of the triangle are endpoints of a diameter of the circle. Calculate the sum of the areas of the two small shaded regions formed outside the triangle but inside the circle, expressed in the form \(a\pi - b\sqrt{c}\). Determine \(a+b+c\).

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