
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
The diagram shows a shaded semicircle of diameter 4, from which a smaller semicircle has been removed. The two semicircles touch at exactly three points. What fraction of the larger semicircle is shaded?

A $\frac{2}{\pi}$  
B $\frac{1}{2}$  
C $\frac{\sqrt{2}}{3}$  
D $\frac{\sqrt{2}}{2}$  
E $\frac{3}{4\pi}$

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