
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 two different points $M(x\_1, y\_1)$ and $N(x\_2, y\_2)$ on the curve of the function $y = f(x)$ with the slopes of the tangents at these points being $k\_M$ and $k\_N$ respectively, the "curvature" $\phi(M, N)$ between points $M$ and $N$ is defined as $\phi(M, N) = \frac{|k\_M - k\_N|}{|MN|}$, where $|MN|$ is the length of the line segment $MN$. For the curve $f(x) = x^3 + 2$, find the range of values of $\phi(M, N)$ for two different points $M(x\_1, y\_1)$ and $N(x\_2, y\_2)$ such that $x\_1 + x\_2 = 2$.

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