
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 functions $f(x) = \ln x+x^2-1$ and $g(x) = e^x - e$,  
(I) Determine the monotonicity of $f(x)$;  
(II) If for any $x \in (1, +\infty)$, $mg(x) > f(x)$ always holds, find the range of real number $m$.

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