
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 circle with radius \( R \), a chord \( AB \) is given. Let \( M \) be an arbitrary point on the circle. On the ray \( MA \), we place a segment \( MN \) such that \(|MN| = R\), and on the ray \( MB \), we place a segment \( MK \), equal to the distance from \( M \) to the orthocenter of triangle \( MAB \). Find \(|NK|\) if the smaller arc subtended by \( AB \) is equal to \( 2\alpha \).

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