
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 triangle \( LOM \) with an angle \( \angle LOM = \alpha^\circ \) is rotated around the point \( O \) by some acute angle. As a result, point \( L \) moves to point \( N \), which lies on the side \( LM \), and point \( M \) moves to point \( K \) such that \( OM \perp NK \). Find the angle of rotation (in degrees).

Note: The values for \( \alpha \) vary: 21, 24, 27, 33, 39, 42, 48, 51, 54, 57, 63, 66, 69, 72, 78.

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