
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 that the moving straight line $l$ passing through point $A(-4,0)$ intersects with the parabola $G$: $x^{2}=2py (p > 0)$ at points $B$ and $C$, when the slope of line $l$ is $\frac{1}{2}$, $\overrightarrow{AC}= \frac{1}{4} \overrightarrow{AB}$.
(I) Find the equation of the parabola $G$;
(II) Let the perpendicular bisector of segment $BC$ intercept the $y$-axis at $b$, find the range of values for $b$.

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