
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
Suppose there are two semicircles \(POQ\) and \(ROS\) inside a larger circle \(O\) such that the diameters of \(POQ\) and \(ROS\) are perpendicular to each other. The radius of \(POQ\) is \(r\), and the radius of \(ROS\) is \(2r\). What is the ratio of the combined areas of the two semicircles to the area of circle \(O\)?
A) \(\frac{1}{4}\)
B) \(\frac{1}{2}\)
C) \(\frac{5}{8}\)
D) \(\frac{3}{4}\)
E) \(1\)

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