
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
Trapezoid \(ABCD\) with base \(AD\) is divided by diagonal \(AC\) into two triangles. A line \(l\), parallel to the base, divides these triangles into two triangles and two quadrilaterals. At what position of line \(l\) is the sum of the areas of the resulting triangles minimized?

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