
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
Two semicircles with radius \(r/2\) each are inscribed in a circle with radius \(r\). The semicircles are positioned so that each semicircle's diameter is a chord of the circle that passes through the circle's center \(O\). What is the ratio of the combined areas of the two semicircles to the area of circle \(O\)?

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