
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
Two circles, $C$ and $D$, are inside circle $E$. The diameter of circle $E$ is 24 cm. Circles $C$ and $D$ are equal in size and do not overlap. What is the diameter of each of circles $C$ and $D$ if the ratio of the shaded area (that is not covered by $C$ or $D$ but is inside $E$) to the total area occupied by circles $C$ and $D$ is 4:1?

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