
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
From point $K$, located outside a circle with center $O$, two tangents $KM$ and $KN$ are drawn to the circle ($M$ and $N$ are the points of tangency). Point $C$ is taken on the chord $MN$ such that $|MC| < |CN|$. Through point $C$, a line perpendicular to segment $OC$ is drawn, intersecting the segment $NK$ at point $B$. It is known that the radius of the circle is $R$, $\Angle MKN = \alpha$, and $|MC|=b$. Find $|CB|$.

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