
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 trapezoid \( ABCD \) with base \( AD \) is cut by diagonal \( AC \) into two triangles. A line \( l \), parallel to the base, cuts 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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