
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
Triangle  $XYZ$  is inside square  $KLMN$  shown below so that its vertices each lie on three different sides of the square. It is known that: $\bullet$  The area of square  $KLMN$  is  $1$ . $\bullet$  The vertices of the triangle divide three sides of the square up into these ratios: $KX : XL = 3 : 2$  $KY : YN = 4 : 1$  $NZ : ZM = 2 : 3$ What is the area of the triangle  $XYZ$ ? (Note that the sketch is not drawn to scale).
![Image](https://cdn.artofproblemsolving.com/attachments/8/0/38e76709373ba02346515f9949ce4507ed4f8f.png)

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