
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 point $P$ be a point on the parabola with ordinate 4, and $|PF|=4$.  
(1) Find the equation of the parabola;  
(2) Let points $A(x_1, y_1)$ and $B(x_2, y_2)$ be two distinct points on the parabola other than point $P$. The angle bisector of $\angle APB$ is perpendicular to the x-axis, and the perpendicular bisector of segment $AB$ intersects the x-axis at point $M$. Find the minimum value of $$\frac {|MF|}{|AB|}$$.

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