
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, if the area of $\triangle ABC$ is 36 where $A(3, 15)$, $B(15, 0)$, and $C(0, q)$ lie on a Cartesian plane. Determine the value of $q$.
[asy]
size(5cm);defaultpen(fontsize(9));
pair a = (3, 15); pair b = (15, 0); pair c = (0, 12);pair d= (3, 0);
draw(a--b--c--cycle);

label("$A(3, 15)$", a, N);
label("$B(15, 0)$", b, S);
label("$C(0, q)$", c, W);
label("$x$", (17, 0), E);
label("$y$", (0, 17), N);
draw((-2,0)--(17,0), Arrow);
draw((0,-2)--(0,17), Arrow);
[/asy]

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