
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
The trapezoid \( ABCD \) with bases \( BC = 2 \) and \( AD = 10 \) is such that both an inscribed circle and a circumscribed circle can be drawn. Determine where the center of the circumscribed circle is located, i.e., whether it is inside, outside, or on one of the sides of the trapezoid \( ABCD \). Also, find the ratio of the radii of the circumscribed and inscribed circles.

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