
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 adjoining diagram, \(AB\) is a diameter of the circle, \(CD\) is a chord parallel to \(AB\), and \(AC\) intersects \(BD\) at \(E\), with \(\angle AED = 90^\circ - \alpha\). Determine 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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