
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 a triangle with a perimeter of \(2p\). A tangent parallel to a side of the triangle is drawn to this circle. Find the maximum possible length of the segment of this tangent that lies inside the triangle.

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