
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
From point \( A \), a secant and a tangent are drawn to a circle with radius \( R \). Let \( B \) be the point of tangency, and \( D \) and \( C \) be the points where the secant intersects the circle, with point \( D \) lying between \( A \) and \( C \). It is known that \( BD \) is the angle bisector of angle \( B \) in triangle \( ABC \) and its length is equal to \( R \). Find the distance from point \( A \) to the center of the circle.

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