
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 line segment $\overline{AB}$ which is 9 units long. Point $C$ divides $\overline{AB}$ such that $\overline{AC} = 6$ units and $\overline{CB} = 3$ units. Semicircles are constructed on $\overline{AC}$ and $\overline{CB}$ as diameters, outside of line segment $\overline{AB}$. A third semicircle is constructed on $\overline{AB}$ as the diameter, outside of $\overline{AB}$. If we also have a perpendicular from $C$ to the diameter of the semicircle on $\overline{AB}$, meeting it at point $D$, calculate the ratio of the shaded area (area of the large semicircle minus the areas of the two smaller semicircles) to the area of a circle with radius $\overline{CD}$.

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