
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
Point \( O \) lies on segment \( AB \) with \( AO = 13 \) and \( OB = 7 \). A circle with center at \( O \) and radius 5 is drawn. Tangents are drawn from points \( A \) and \( B \) to this circle, intersecting at point \( M \), with the points of tangency lying on the same side of line \( AB \). Find the radius of the circumcircle of triangle \( AMB \).

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