
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 $y^{2}=2px(p > 0)$ with a point $Q(4,m)$ on it, the distance from $Q$ to the focus $F$ is $5$,

$(1)$ Find the values of $p$ and $m$.

$(2)$ A line $L$ passing through the focus $F$ intersects the parabola at points $A$ and $B$. If $|AB|=8$, find the equation of line $L$.

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