
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
\( AB \) and \( AC \) are tangents to a circle with center \( O \), \( M \) is the point of intersection of the line \( AO \) with the circle; \( DE \) is the segment of the tangent drawn through the point \( M \) between \( AB \) and \( AC \). Find \( DE \), if the radius of the circle is 15 and \( AO = 39 \).

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