
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 a parabola $y^2 = 2px$ ($p > 0$) with focus $F$, let $A$ and $B$ be two moving points on the parabola such that $\angle AFB = 60^\circ$. Let $M$ be the midpoint of $AB$, and draw a perpendicular line $MN$ from $M$ to the parabola's axis, with foot $N$. Find the maximum value of $\frac{|MN|}{|AB|}$.

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