
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 square is inscribed in a circle with a diameter of 16 cm. Two arcs are shaded within the circle starting from the midpoints of two adjacent sides of the square to the closest vertices forming pie-shaped regions. Calculate the sum of the area of these two shaded regions, given that the area is expressible in the form \(a\pi - b\sqrt{c}\). What is the sum \(a+b+c\)?

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