
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 function $y=f(x)$ has a graph where two distinct points $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$ have slopes of their tangents $k_{M}$ and $k_{N}$ respectively. Define $\varphi(M,N)= \frac {|k_{M}-k_{N}|}{|MN|}$ (where $|MN|$ is the length of segment $MN$) as the "curvature" of the curve $y=f(x)$ between points $M$ and $N$.  
(1) For the function $f(x)=x^{3}+1$, with the $x$-coordinates of points $M$ and $N$ being $1$ and $2$ respectively, find $\varphi(M,N)=$ ______;  
(2) Suppose on the curve $f(x)=x^{3}+2$, two distinct points $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$ exist, and $x_{1} \cdot x_{2}=1$, then the range of $\varphi(M,N)$ is ______.

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