
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
In square $WXYZ$, angle $W$ is trisected by $\overline{WP}$ and $\overline{WQ}$, where $P$ is on $\overline{XY}$, $Q$ is on $\overline{WZ}$, $YP=4$, and $QZ=3$. Find the area of $WXYZ$.

[asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8)); dotfactor=4;
real length = 2 * (4*sqrt(3) - 3), width = 4*sqrt(3);
draw(origin--(length,0)--(length,width)--(0,width)--cycle);
draw((length,width)--(0,3)^^(length,width)--(length - 4,0));
dot("$W$",origin,SW); dot("$X$",(length,0),SE); dot("$Y$",(length,width),NE); dot("$Z$",(0,width),NW); 
dot("$Q$",(0,3),W); dot("$P$",(length - 4,0),S);
[/asy]

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