
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, $ABCD$ is a trapezoid with an area of $20$. $CD$ is three times the length of $AB$. A line segment $CE$ is drawn from point $C$ to meet $AB$ extended at point $E$, such that $AE = AD$. What is the area of $\triangle ACD?$

[asy]
draw((0,0)--(-3,4)--(9,4)--(12,0)--cycle);
draw((0,0)--(9,4));
label("$D$",(0,0),W);
label("$A$",(-3,4),NW);
label("$B$",(9,4),NE);
label("$C$",(12,0),E);
label("$E$",(-6,4),NW);
[/asy]

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