
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]


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The bases of an isosceles trapezoid are in the ratio 3:2. A circle is constructed on the larger base as its diameter, and this circle intersects the smaller base such that the segment cut off on the smaller base is equal to half of the smaller base. In what ratio does the circle divide the non-parallel sides of the trapezoid?

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