
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 $C:y^{2}=2px\left(p \gt 0\right)$ with the focus $F$ at a distance of $4$ from the directrix. Points $M(x_{1}$,$y_{1})$ and $N(x_{2}$,$y_{2})$ lie on the parabola $C$. If $(y_{1}-2y_{2})(y_{1}+2y_{2})=48$, find $\frac{|MF|}{|NF|}$.

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