
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 $C: y^2 = 4x$ with focus $F$, and a line $l$ passing through point $P(-1, 0)$ with slope $k$ ($k > 0$) intersects the parabola $C$ at points $A$ and $B$. The lines $AF$ and $BF$ intersect the parabola $C$ again at points $M$ and $N$ respectively. If $\frac {|AF|}{|FM|} + \frac {|BF|}{|FN|} = 18$, then $k = \_\_\_\_\_\_$.

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