
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
Given semicircles $ABC$ and $DEF$ are inscribed inside circle $O$ such that each semicircle's diameter forms a chord of circle $O$. The radius of semicircle $ABC$ is $\frac{2}{3}$ the radius of circle $O$. Calculate the ratio of the combined areas of the two semicircles to the area of circle $O$, if both semicircles have the same radius.

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