
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 \( A B C \), angle \( B \) is a right angle, and \( A B = B C = 2 \). A circle touches both legs at their midpoints and intersects the hypotenuse at chord \( D E \). Find the area of triangle \( B D E \).

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