
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. What is the area of triangle $BCD$ if the length of segment $CD$ is 39 units?

[asy]
draw((0,0)--(39,0)--(10,18)--(0,0)); // Adjusted for new problem length
dot((0,0));
label("$A$",(0,0),SW);
label("9",(4.5,0),S); // New base length of ABC
dot((9,0));
label("$C$",(9,0),S);
label("39",(24,0),S); // New length for CD
dot((39,0));
label("$D$",(39,0),SE);
dot((10,18)); // Adjusted location of B to maintain proportionality
label("$B$",(10,18),N);
draw((9,0)--(10,18));
[/asy]

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