
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
Pentagon ABCDE has a vertical line of symmetry. What is the new $y$-coordinate of vertex C so that the area of the pentagon is 100 square units? The vertices B and D are now at $(0,6)$ and $(6,6)$ respectively, while A and E are at $(0,0)$ and $(6,0)$. [asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(0,0), B=(0,6), C=(3,?), D=(6,6), E=(6,0);
pair[] dots={A,B,C,D,E};

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

axes(Arrows(4));

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

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