
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 an inscribed quadrilateral $ABCD$ with perpendicular diagonals. On its circumscribing circle, there is a point $E$ diametrically opposite to $D$, such that segments $AB$ and $DE$ do not intersect. Find the ratio of the areas of triangle $BCD$ and quadrilateral $ABED$.

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