
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
The curvature $\varphi(M,N)$ of a curve $y=f(x)$ between two different points $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$ on its graph, where the slopes of the tangents at $M$ and $N$ are $k_{M}$ and $k_{N}$ respectively, is defined as $\varphi(M,N)=\frac{|k_{M}-k_{N}|}{|MN|}$ (where $|MN|$ is the length of the segment $MN$). For the curve $f(x)=x^{3}+2$ with two different points $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$ on it, and given that $x_{1}x_{2}=1$, the range of $\varphi(M,N)$ is ______.

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