
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
In the given circle, $AB$ is a diameter. Chord $CD$ is parallel and at a distance from $AB$. The chords $AC$ and $BD$ intersect at $E$. If $\angle AED = \alpha$, and $\angle BOC = 2\alpha$ where $O$ is the center of the circle, find the ratio of the area of $\triangle CDE$ to that of $\triangle ABE$.

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