
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
The square shown has a side of 20 cm and is circumscribed around a circle. Two of its diagonals form an isosceles triangle with the circle's center. If the sum of the areas of the two small shaded regions in square centimeters is $a\pi - b\sqrt{c}$, what is $a+b+c$? Assume all necessary angles are standard angles for such a configuration.

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