
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 triangle has a perimeter \( 2p \) and an inscribed circle. A tangent to this circle, parallel to one side of the triangle, is drawn. Find the maximum possible length of the segment of this tangent that lies within the triangle.

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