
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 depicted is an equilateral triangle with side length 15 cm. A side of the triangle is the diameter of the circle. Calculate the sum of the areas of the two small shaded regions within the circle in square centimeters. Express your answer in terms of $\pi$ and in simplest radical form as $a\pi - b\sqrt{c}$. Determine the value of $a+b+c$ for this context.

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