
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 $\triangle QCA$ in terms of $p$. Your answer should be simplified as much as possible.
[asy]
size(5cm);defaultpen(fontsize(9));
pair o = (0, 0); pair q = (0, 15); pair b = (15, 0);
pair a = (3, 15); pair t = (3, 0); pair c = (0, 9);

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

label("$Q(0, 15)$", q, W);
label("$A(3, 15)$", a, NE);
label("$B(15, 0)$", b, S);
label("$O(0, 0)$", o, SW);
label("$x$", (18, 0), E);
label("$y$", (0, 18), N);
//label("$T(3, 0)$", t, S + 0.6 * E);
label("$C(0, p)$", c, W);
[/asy]

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