
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 point $P$ on the parabola $x^{2}=2y$, draw a line $PQ$ perpendicular to the $x$-axis with foot $Q$. Let $M$ be the midpoint of $PQ$.
(I) Find the equation of the locus $E$ of point $M$.
(II) Let point $S(-4,4)$, and a line $l$ through $N(4,5)$ intersects the locus $E$ at points $A$ and $B$. If the slopes of lines $SA$ and $SB$ are $k_{1}$ and $k_{2}$ respectively, find the minimum value of $|k_{1}-k_{2}|$.

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