
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 $C$: $y^{2}=2px (p > 0)$ passing through point $A(1,m)$, $B$ is the intersection point of the parabola's axis and the $x$-axis. If $|AB|=2 \sqrt {2}$, find:

1. The equation of the parabola.
2. Take any point $P(x_{0},2)$ on the parabola, draw two lines passing through point $P$ intersecting the parabola at points $M$ and $N$ respectively. Connect $MN$, and let the slopes of lines $PM$, $PN$, and $MN$ be $k_{1}$, $k_{2}$, and $k_{3}$ respectively. Find the value of $\frac {1}{k_{1}}+ \frac {1}{k_{2}}- \frac {1}{k_{3}}$.

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