
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 the triangular pyramid \(S A B C\), two equal lateral faces \(A S B\) and \(C S B\) are perpendicular to the base plane, and the face \(A S C\) is inclined to the base plane at an angle \(\beta\). Find the radius of the sphere circumscribed around the pyramid if the radius of the circle circumscribed around the base is \(r\) and \(\angle A B C = \alpha\).

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