
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
A circle has a diameter AB that measures 10 cm. At point C, perpendicular to AB and also lying on the circle, section off the circle into two segments. Consider the right triangle ACB with the right angle at C. Calculate the sum of the areas of the two shaded segments within the circle but outside triangle ACB. Give your answer in the form $a\pi - b\sqrt{c}$ and find $a+b+c$.

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