
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. The triangle's side is the diameter of the circle. In two opposite sectors of the circle, there are small shaded regions. If the sum of the areas of the two small shaded regions is in the form \(a\pi - b\sqrt{c}\), calculate \(a+b+c\).

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