
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 provided, if the area of $\triangle ABC$ is 36, what is the value of $q$? [asy]
size(5cm);defaultpen(fontsize(9));
pair o = (0, 0); pair a = (0, 12); pair b = (15, 0);
pair q = (3, 12); pair c = (0, 8);

draw((-2, 0)--(18, 0), Arrow);
draw((0, -2)--(0, 15), Arrow);
draw(a--q--b);
draw(a--c--b);

label("$A(0, 12)$", a, W);
label("$Q(3, 12)$", q, NE);
label("$B(15, 0)$", b, S);
label("$O(0, 0)$", o, SW);
label("$x$", (18, 0), E);
label("$y$", (0, 15), N);
label("$C(0, q)$", c, W);
[/asy]

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