
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 the diagram, the area of triangle $ABC$ is 36 square units. Point $E$ is on line $AD$ such that $DE = 10$ units. What is the area of quadrilateral $BCED$?

[asy]
draw((0,0)--(40,0)--(12,18)--(0,0));
dot((0,0));
label("$A$",(0,0),SW);
label("8",(4,0),S);
dot((8,0));
label("$C$",(8,0),S);
label("32",(20,0),S);
dot((40,0));
label("$D$",(40,0),SE);
dot((12,18));
label("$B$",(12,18),N);
dot((30,0));
label("$E$",(30,0),SE);
draw((8,0)--(12,18));
draw((30,0)--(12,18));
[/asy]

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