
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 $p$ given the points $Q(0, 12)$, $A(3, 12)$, $C(0, p)$, and $B(12, 0)$ in the coordinate plane. Assume $\triangle QCA$ is right-angled at $C$.

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