
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 a parabola $C$: $y^{2}=2px$ with a focus at $F$, one of the intersection points of parabola $C$ and line $l_{1}$: $y=-x$ has an x-coordinate of $8$.
(I) Find the equation of parabola $C$;
(II) A line $l_{2}$, passing through the origin, is perpendicular to $l_{1}$ and intersects the parabola at two distinct points $A$ and $B$. If the midpoint of segment $AB$ is $P$, and $|OP|=|PB|$, find the area of triangle $FAB$.

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