
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 an isosceles triangle \(ABC\), the angle at vertex \(B\) is \(\alpha\). A tangent is drawn at point \(C\) to the circumcircle of this triangle, intersecting the extension of the angle bisector \(BD\) of angle \(B\) at point \(E\). Find the ratio of the area of triangle \(CDE\) to the area of triangle \(ABC\).

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