Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: The triangle shown is an equilateral triangle with side length 12 cm. A side of the triangle is the diameter of the circle. If the sum of the areas of the two small shaded regions in square centimeters in simplest radical form is $a\pi - b\sqrt{c}$, what is $a+b+c$? [asy]
import graph;
size(2inch);
pair A = dir(60);
pair B = dir(240);
pair C = dir(0);
pair D = dir(300);
pair E = extension(A, C, B, D);
draw(A--B); draw(A--E); draw(B--E);
draw(Circle( (0,0), 1));
fill(Arc((0,0), C, A)--cycle, gray);
fill(Arc((0,0), B, D)--cycle, gray);
[/asy]
user