
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 a point \( M \), lying outside a circle with center \( O \) and radius \( R \), tangents \( MA \) and \( MB \) are drawn (\( A \) and \( B \) are the points of tangency). Lines \( OA \) and \( MB \) intersect at point \( C \). Find \( OC \), given that the segment \( OM \) is bisected by the circle.

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