
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
The base \( AC \) of an isosceles triangle \( ABC \) is a chord of a circle whose center lies inside triangle \( ABC \). The lines passing through point \( B \) are tangent to the circle at points \( D \) and \( E \). Find the area of triangle \( DBE \) if \( AB = BC = 2 \), \( \angle B = 2 \arcsin \frac{1}{\sqrt{5}} \), and the radius of the circle is 1.

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