
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 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 the line is \\(\dfrac{1}{2}\\), \\(\overrightarrow{AC}=4\overrightarrow{AB}\\).
\\((1)\\) Find the equation of the parabola \\(G\\);
\\((2)\\) Let the perpendicular bisector of segment \\(BC\\) have a \\(y\\)-intercept of \\(b\\), find the range of \\(b\\).

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