
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
A sphere with center $O$ is inscribed in a trihedral angle with vertex $S$ and touches its faces at points $K, L, M$ (all plane angles of the trihedral angle are different). Find the angle $K S O$ and the area of the cross-section of this trihedral angle by plane $K L M$, given that the areas of the cross-sections of the trihedral angle by planes tangent to the sphere and perpendicular to line $S O$ are 4 and 9.

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