
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 of a function $y=f(x)$ between two distinct points $M(x_1, y_1)$ and $N(x_2, y_2)$ on its graph, with slopes of the tangents at these points being $k_M$ and $k_N$ respectively, is defined as $\varphi(M, N) = \frac {|k_M - k_N|}{|MN|}$ (where $|MN|$ is the length of the line segment MN).  
1. For the function $f(x) = x^3 + 1$, if the x-coordinates of points M and N are 1 and 2 respectively, find $\varphi(M, N)$.  
2. Suppose on the curve $f(x) = x^3 + 2$, there are two distinct points $M(x_1, y_1)$ and $N(x_2, y_2)$, and $x_1 \cdot x_2 \neq 1$, determine the range of values for $\varphi(M, N)$.

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