
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 functions $f(x)=\ln x$ and $g(x)=0.5x^{2}-bx$ (where $b$ is a constant),

$(1)$ The tangent line to the graph of the function $f(x)$ at the point $(1,f(1))$ is tangent to the graph of the function $g(x)$. Find the value of the real number $b$;

$(2)$ If the function $h(x)=f(x)+g(x)$ is not monotonic over its domain, find the range of values for the real number $b$;

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