
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 $f(x)=mx- \dfrac {m}{x}$, $g(x)=2\ln x$.  
(I) When $m=1$, determine whether the equation $f(x)=g(x)$ has real roots in the interval $(1,+\infty)$.  
(II) If for $x\in(1,e]$ the inequality $f(x)-g(x) < 2$ always holds, find the range of the real number $m$.

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