
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
Determine an expression for the area of $\triangle PRD$ in terms of $q$. [asy]
size(5cm);defaultpen(fontsize(9));
pair p = (0, 12); pair d = (12, 0);
pair r = (4, 12); pair t = (4, 0); pair c = (12, 9);

draw((-2, 0)--(15, 0), Arrow);
draw((0, -2)--(0, 15), Arrow);
draw(p--r--d);
draw(r--c--d);

label("$P(0, 12)$", p, W);
label("$R(4, 12)$", r, NE);
label("$D(12, 0)$", d, S);
label("$O(0, 0)$", o, SW);
label("$x$", (15, 0), E);
label("$y$", (0, 15), N);
label("$C(12, q)$", c, E);
[/asy]

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