
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
A circle with center O has a radius of 10 units. Inside this circle, two semicircles are formed with diameters that lie along two perpendicular diameters of the circle. What is the ratio of the combined areas of the two semicircles to the area of the circle?
A) \(\frac{1}{8}\)
B) \(\frac{1}{6}\)
C) \(\frac{1}{4}\)
D) \(\frac{1}{3}\)
E) \(\frac{1}{2}\)

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