
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 $f(x)=m\ln x+\dfrac{3}{2}x^{2}-4x$.

$(1)$ If the tangent line of the curve $y=f(x)$ at $x=1$ is perpendicular to the $y$-axis, find the extreme values of the function $f(x)$;

$(2)$ Let $g(x)=x^{3}-4$, if $h(x)=f(x)-g(x)$ is monotonically decreasing on $(1,+\infty)$, find the range of the real number $m$.

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