
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 a trihedral angle, all plane angles of which are equal to $\alpha$, a sphere is placed such that it touches all the edges of the trihedral angle. The faces of the trihedral angle intersect the sphere along circles with radius $r$. Find the radius of the sphere.

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