
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
Let \(B\) be a point on the x-axis at \(B(x, 0)\) and \(Q\) at \(Q(0, 15)\) on the y-axis, where \(x > 0\). Point \(C\) is on the y-axis at \(C(0, p)\) such that \(0 < p < 15\). Find an expression for the area of triangle \(COB\) in terms of \(p\) and \(x\). Illustrate the problem as shown:

[asy]
size(6cm);
defaultpen(fontsize(10));
pair o = (0, 0);
pair q = (0, 15);
pair b = (18, 0);
pair c = (0, 9);

draw((-2, 0)--(20, 0), Arrow);
draw((0, -2)--(0, 20), Arrow);
draw(q--b--o--cycle);
draw(c--b);

label("$Q(0, 15)$", q, W);
label("$B(x, 0)$", b, S);
label("$O(0, 0)$", o, SW);
label("$x$", (20, 0), E);
label("$y$", (0, 20), N);
label("$C(0, p)$", c, W);
[/asy]

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