
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
In the diagram below, triangle \( \triangle ABC \) is an equilateral triangle and \( CD \) is both an altitude of the triangle and a diameter of the circle. If \( AB = 10 \) cm, determine the shaded area.

![Diagram](https://cdn.mathpix.com/cropped/2024_05_01_4747cb56a5540358921fg-02.jpg?height=426&width=491&top_left_y=495&top_left_x=680)

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