
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
An isosceles triangle \( ABC \) is inscribed in a circle, where \( AB = BC \) and \(\angle B = \beta\). The midline of the triangle is extended to intersect the circle at points \( D \) and \( E \) (with \( DE \parallel AC \)). Find the ratio of the areas of triangles \( ABC \) and \( DBE \).

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