
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
Point \( D(0, kp) \) lies on the \( y \)-axis between \( Q(0,24) \) and \( O(0,0) \), where \( k \) is a fraction such that \( 0 < k < 1 \). Determine an expression for the area of \( \triangle DOB \) in terms of \( p \) and \( k \). [asy]
size(5cm); defaultpen(fontsize(9));
pair o = (0, 0); pair q = (0, 24); pair b = (24, 0);
pair d = (0, 18); 

draw((-2, 0)--(26, 0), Arrow);
draw((0, -2)--(0, 26), Arrow);
draw(b--o--d, dashed);
draw(d--b);

label("$Q(0, 24)$", q, W);
label("$B(24, 0)$", b, S);
label("$O(0, 0)$", o, SW);
label("$x$", (26, 0), E);
label("$y$", (0, 26), N);
label("$D(0, kp)$", d, W);
[/asy]

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