
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
A circle is inscribed in an isosceles triangle. The points of tangency divide each of the equal sides into segments of length \( \boldsymbol{m} \) and \( \boldsymbol{n} \), counting from the vertex. Three tangents are drawn to the circle, each parallel to one side of the triangle. Determine the lengths of the segments of the tangents that are enclosed between the sides of the triangle.

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