
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
Given that the sine value of the inclination angle of the line $l$ (with a slope greater than 0) is $\frac{{\sqrt{2}}}{2}$, and the intercept on the $x$-axis is $-2$, the line $l$ intersects the parabola $C: x^{2}=2py\left(p \gt 0\right)$ at points $A$ and $B$. If $|AB|=16$, then $p=$____.

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