
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. Points $A$, $B$, and $C$ are positioned in such a way that $A$ and $C$ are on the base $AD$ of a trapezoid $ABCD$, with $A$ at $(0,0)$, $D$ at $(40,0)$, and $B$ at $(10,24)$. Line segment $BC$ is parallel to $AD$ and $C$ is located at $(30,0)$. What is the area of triangle $BCD$?

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