
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 $\triangle QDA$ in terms of $p$, where $D$ is a point on the y-axis below $Q$ but above $O$. The coordinates are \( Q(0, 15) \), \( A(5, 15) \), \( B(15, 0) \), and \( D(0, p) \) with \( 0 < p < 15 \).

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