
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
Given the trapezoid $ABCD$ with $BC \parallel AD$, draw the line $XY$ in the trapezoid that is parallel to $BC$ and $AD$ such that the trapezoids $AXYD$ and $XBCY$ have equal perimeters. In what ratio does this line divide the area of the trapezoid?

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