
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
Given four points \( A, B, C, D \) that do not lie in the same plane. A sphere is tangent to lines \( AB \) and \( AD \) at point \( A \), and to lines \( BC \) and \( CD \) at point \( C \). Find the surface area of the sphere, given that \( AB = 1 \), \( BD = 2 \), and \( \angle ABC = \angle BAD = 90^\circ \).

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