
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 $x^{2}=2y$, a moving point $P$ is taken, and two tangent lines are drawn from $P$ intersecting the parabola at points $A$ and $B$, respectively. Additionally, $k_{PA}k_{PB}=-2$.
(I) Find the trajectory equation of point $P$;
(II) Determine if line $AB$ always passes through a fixed point. If it does, find the coordinates of this fixed point; otherwise, provide a reason.

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