
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 $C$: $y^{2}=2px(p > 0)$, whose directrix is the line $l$: $x=-2$, and its focus is $F$.  
$(1)$ Find the equation of the parabola $C$.  
$(2)$ If $l$ intersects the $x$-axis at point $A$, and point $M$ is on the parabola $C$, and the distance from $M$ to the focus $F$ is $8$, find the area $S$ of $\triangle AFM$.

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