
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 $f(x)=\ln x+(a-2)x$, the curve corresponding to the function $y=f(x)$ has a tangent line at point $(1,f(1))$ that is parallel to the $x$-axis.

(1) Find the value of $a$ and the maximum value of $f(x)$;

(2) Let $m > 0$, the function $g(x)=\frac{1}{3}m{x}^{3}-mx,x\in (1,2)$, if for any $x_1 \in (1,2)$, there exists $x_2 \in (1,2)$ such that $f(x_1)-g(x_2)=0$, find the range of values of the real number $m$.

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