
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 the parabola $y^{2}=2px(p > 0)$ with focus $F$, and a point $P$ on the parabola with an ordinate of $4$, and $|PF|=4$.
- (I) Find the equation of the parabola;
- (II) Let points $A(x_{1},y_{1})$, $B(x_{2},y_{2})$ ($y_{i}\leqslant 0,i=1,2$) be two points on the parabola, and the angle bisector of $\angle APB$ is perpendicular to the x-axis. Find the equation of line $AB$ when the area of $\triangle PAB$ is maximized.

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