
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
Given an isosceles triangle ABC with AB = AC = 20 cm and BC = 12 cm lying inside a circle, where side BC is the diameter of the circle. A side of the triangle, BC, subtends two arcs at A forming shaded regions within the circle. Calculate the sum of the areas of these two shaded regions. The area expression is in simplest radical form as \(a\pi - b\sqrt{c}\). What is \(a+b+c\)?

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