
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 $f(x)=\ln x$ and $g(x)=x^{2}$.
(I) Find the maximum value of the function $h(x)=f(x)-x+1$.
(II) For any $x_{1}$, $x_{2}\in(0,+\infty)$, and $x_{2} < x_{1}$, does there exist a real number $m$ such that $mg(x_{2})-mg(x_{1}) > x_{1}f(x_{1})-x_{2}f(x_{2})$ always holds true? If so, find the range of $m$; if not, explain the reason.

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