
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 50 square units. $C$ is moved to the right such that $BC=8$ and the total distance from $B$ to $D$ horizontally is $40$. Calculate the area of triangle $BCD$.

[asy]
draw((0,0)--(40,0)--(11,20)--(0,0));
dot((0,0));
label("$A$",(0,0),SW);
label("8",(5,0),S);
dot((8,0));
label("$C$",(8,0),S);
label("32",(24,0),S);
dot((40,0));
label("$D$",(40,0),SE);
dot((11,20));
label("$B$",(11,20),N);
draw((8,0)--(11,20));
[/asy]

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