
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 $C$: $y^{2}=2px (p > 0)$ with focus $F$, directrix $x=-1$, and a point $M$ on the directrix below the $x$-axis. A line $l$ passing through $M$ and $F$ intersects with $C$ at point $N$, and $F$ is the midpoint of segment $MN$.

1. Find the equations of parabola $C$ and line $l$.
2. If line $l$ intersects with parabola $C$ at another point $P$ (different from $N$), find the length of segment $PN$.

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