
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 $f(x)=a\ln x-ax-3 (a\in R)$.
(1) Find the monotonic intervals of the function $f(x)$;
(2) The slope of the tangent line to the curve $y=f(x)$ at $x=4$ is $\frac{3}{2}$, and if the function $g(x)=\frac{1}{3}x^{3}+x^{2}[f′(x)+\frac{m}{2}]$ is not monotonic on the interval $(1,3)$, find the range of values of $m$.

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