
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 $C$: $y^{2}=2px (p > 0)$, the distance from its focus $F$ to its directrix is $2$. The line $l$ intersects the parabola $C$ at points $A$ and $B$.
(1) Find the equation of the parabola $C$, the coordinates of the focus, and the equation of the directrix.
(2) If the line $l$ passes through the focus $F$ of the parabola, find the equation of the line $l$ when the length of the segment $AB$ is $5$.

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