
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 a circle with radius 10 units, and two semicircles within it, one with radius 8 units and another with radius 6 units, both passing through the center of the circle, determine the ratio of the combined areas of these two semicircles to the area of the larger circle.

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