
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 leg into segments of lengths \( m \) and \( p \) starting from the vertex. Three tangents parallel to each side of the triangle are drawn to the circle. Find the lengths of the segments of the tangents enclosed between the sides of the triangle.

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