
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
Hexagon ABCDEF has a vertical line of symmetry. What is the $y$-coordinate of vertex D so that the area of the hexagon is 90 square units? [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(2,6), D=(2,22), E=(4,6), F=(4,0);
pair[] dots={A,B,C,D,E,F};

draw(B--C--D--E--F);
dot(dots);

axes(Arrows(4));

label("A(0,0)",A,SW);
label("F(4,0)",F,SE);
label("E(4,6)",E,NE);
label("D",D,NE);
label("C(2,6)",C,N);
label("B(0,6)",B,NW);
[/asy]

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