
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
Quadrilateral ABCD has a horizontal line of symmetry. What is the $y$-coordinate of vertex B so that the area of the quadrilateral is 72 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(8,0), C=(8,16), D=(0,16);
pair[] dots={A,B,C,D};

draw(A--B--C--D--cycle);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("B(8,0)",B,SE);
label("C(8,16)",C,NE);
label("D(0,16)",D,NW);
[/asy]

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