
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
Point $P$ is on the parabola $x^{2}=2y$. A line $PQ$ is drawn through point $P$ perpendicular to the $x$-axis, with foot $Q$. Let $\overrightarrow{PM} = \frac{1}{2} \overrightarrow{PQ}$.

(I) Find the equation of the trajectory $E$ of point $M$.

(II) Let point $S(-4,4)$, and a line $l$ passing through point $N(4,5)$ intersects trajectory $E$ at points $A$ and $B$. Let the slopes of lines $SA$ and $SB$ be $k_{1}$ and $k_{2}$, respectively. Find the value of $k_{1}k_{2}$.

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