
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
[asy] 
fill(circle((4,0),4),grey); 
fill((0,0)--(8,0)--(8,-4)--(0,-4)--cycle,white); 
fill(circle((6,0),2),white); 
fill(circle((3,0),3),white); 
fill(circle((2,0),1),white); 
draw((0,0)--(8,0),black+linewidth(1)); 
draw((6,0)--(6,sqrt(28)),black+linewidth(1)); 
MP("A", (0,0), W);  
MP("B", (8,0), E);  
MP("C", (6,0), S); 
MP("D",(6,sqrt(28)), N); 
[/asy]
In this diagram, four semi-circles are constructed on diameters $\overline{AB}$, $\overline{AC}$, $\overline{CB}$, and a smaller one on $\overline{AE}$ (where $\overline{AE} = \frac{1}{3}\overline{AB}$) such that all are mutually tangent. If $\overline{CD} \bot \overline{AB}$, determine the ratio of the shaded area to the area of a circle with $\overline{CD}$ as radius.

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