
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
The lateral sides \(KL\) and \(MN\) of the trapezoid \(KLMN\) are 15 and 12, respectively, and the base \(LM = 3\). The angle bisector of \(\angle N K L\) passes through the midpoint of the side \(MN\). Find the area of the trapezoid. Answer: 80.

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