
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 function $g(x)=\ln x+\frac{1}{2}x^{2}-(b-1)x$.

    (1) If the function $g(x)$ has a monotonically decreasing interval, find the range of values for the real number $b$;

    (2) Let $x_{1}$ and $x_{2}$ ($x_{1} < x_{2}$) be the two extreme points of the function $g(x)$. If $b\geqslant \frac{7}{2}$, find the minimum value of $g(x_{1})-g(x_{2})$.

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