
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
It is known that in the trapezoid \(ABCD\), where the diagonal \(BD\) forms an angle of \(45^\circ\) with the base, it is possible to inscribe a circle and circumscribe a circle around it. Find the ratio of the area of the trapezoid to the area of the circle inscribed in it. Find the ratio of the area of the trapezoid to the area of the circle circumscribed around it.

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