
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 $C: y^{2}=2px$ $(p > 0)$ with focus $F$, and its directrix intersects the $x$-axis at point $M$. A line $l$ passing through point $M$ with slope $k$ intersects the parabola $C$ at two points $A,B$. If $|AM|=\frac{5}{4}|AF|$, find $k$.

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