
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 $f(x)=mx-\frac{m}{x}$ and $g(x)=3\ln x$,  
(1) When $m=4$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(2,f(2))$;  
(2) If for $x\in(1, \sqrt{e}]$ (where $e$ is the base of the natural logarithm) the inequality $f(x)-g(x) < 3$ always holds, determine the range of the real number $m$.

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