
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
Points \( C \) and \( D \) are taken on a circle with diameter \( AB \). The line \( CD \) and the tangent to the circle at point \( B \) intersect at point \( X \). Express \( BX \) in terms of the radius of the circle \( R \) and the angles \( \varphi = \angle BAC \) and \( \psi = \angle BAD \).

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