
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
In the plane Cartesian coordinate system $xOy$, there is a circle $C:(x+2)^{2}+(y-m)^{2}=3$. If circle $C$ has a chord $AB$ with a midpoint $G$, and the length of $AB$ is twice the distance from $G$ to the center $O$ of circle $C$, i.e., $|AB|=2|GO|$, then the range of the real number $m$ is ______________.

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