
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 $y^{2}=2px (p > 0)$ with focus $F$, let $P(2,y_{0})$ be a point on the parabola. The tangent line $l$ at point $P$ is drawn, as well as a line $m$ parallel to the $x$-axis through $P$. A line parallel to $l$ is drawn through $F$, intersecting $m$ at $M$. If $|PM|=5$, determine the value of $p$.

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