
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
Given a line segment $\overline{AB}$ of length 10 units, place point $C$ on $\overline{AB}$ such that $\overline{AC} = 3$ units and $\overline{CB} = 7$ units. Construct semicircles on $\overline{AB}$, $\overline{AC}$, and $\overline{CB}$ with diameters along the line segment, so that they are mutually tangent. Extend a line perpendicular from $C$ to meet the semicircle on $\overline{AB}$ at point $D$. Calculate the ratio of the shaded area (the area between the semicircles but within the largest semicircle) to the area of the circle with diameter $\overline{CD}$.

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