
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
Three parallel lines touch the sphere with center at point \( O \) in points \( K \), \( L \), and \( M \). It is known that the radius of the sphere is 5, the area of triangle \( OKL \) is 12, and the area of triangle \( KLM \) is greater than 30. Find the angle \( \angle KML \).

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