
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 has a side length of 18 cm and is inscribed in a circle such that one side of the triangle is the diameter of the circle. Calculate the sum of the areas of two shaded regions within the circle but outside the triangle, given that the sum of the areas of these regions, in square centimeters in simplest radical form, is $a\pi - b\sqrt{c}$. What is $a+b+c$?

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