
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
Consider a regular octagon inscribed in a circle. The side length of the octagon is 10 cm. Four of the eight triangular segments, which form by connecting the vertices of the octagon to the center of the circle, are shaded. What is the number of square centimeters in the area of the shaded regions? Express your answer in simplest radical form.

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