
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
Circle $C$ is within circle $D$. The diameter of circle $D$ is 20 cm. Determine the diameter of circle $C$ such that the ratio of the shaded area (area of $D$ but outside $C$) to the area of circle $C$ is 2:1.

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