
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 $E: y^2 = 4x$ with focus $F$, a line $l$ passing through point $F$ intersects the parabola at points $A$ and $B$, and intersects the y-axis at point $C$, with $O$ being the coordinate origin.
$(1)$ If $k_{OA} + k_{OB} = 4$, find the equation of line $l$;
$(2)$ The perpendicular bisector of segment $AB$ intersects line $l$, the x-axis, and the y-axis at points $D$, $M$, and $N$, respectively. Find the minimum value of $\frac{S_{\triangle NDC}}{S_{\triangle FDM}}$.

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