
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
Through the focus of the parabola ${{x}^{2}}=2py (p > 0 )$, a line with a slope of $1$ intersects the parabola at points $A$ and $B$. The orthogonal projections of $A$ and $B$ on the $x$-axis are $D$ and $C$, respectively. If the area of trapezoid $ABCD$ is $12 \sqrt{2}$, then $p=$ ______.

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