
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 point $F$ is the intersection point of the parabola $C$: $y^{2}=2px (p > 0)$ and line $l_{1}$: $y=-x$. The x-coordinate of one intersection point of line $l_{1}$ and parabola $C$ is $8$.
1. Find the equation of parabola $C$.
2. Line $l_{2}$ passes through the origin, is perpendicular to $l_{1}$, and intersects with parabola $C$ at two distinct points $A$ and $B$. If the midpoint of line segment $AB$ is $P$ and $|OP|=\frac{1}{2}|AB|$, find the area of $\triangle FAB$.

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