
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 $\triangle ACD$ in terms of $p$, where $A$ and $D$ are points on the x-axis at coordinates $(2, 0)$ and $(t, 0)$ respectively, and point $C$ is at $(0, p)$, with $0 < p < 12$ and $0 < t < 12$.

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