
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
On the sides of a unit square, points \( K, L, M, \) and \( N \) are marked such that line \( KM \) is parallel to two sides of the square, and line \( LN \) is parallel to the other two sides of the square. The segment \( KL \) cuts off a triangle from the square with a perimeter of 1. What is the area of the triangle cut off from the square by the segment \( MN \)?

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