
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, and $CD$ is a chord parallel to $AB$. The diagonal $AC$ intersects diagonal $BD$ at point $E$. If $\angle BED = \beta$ where $BE$ and $ED$ are not radii, find the ratio of the area of $\triangle ABE$ to that of $\triangle CDE$.

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