
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 the definition of a function $y=f(x)$ in the set $U$, if for any $x\_1$, $x\_2∈U$, we have $|f(x\_1)-f(x\_2)| < 1$, then the function $y=f(x)$ is called a $storm$ function in $U$.
(I) Determine whether the following functions are $storm$ functions in $[-1,1]$, and explain the reasons:
$①y=2^{x-1}+1$, $②y= \frac {1}{2}x^{2}+1$;
(II) If the function $f(x)= \frac {1}{2}x^{2}-bx+1$ is a $storm$ function in $x∈[-1,1]$, find the range of values for $b$.

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