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

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