
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 $f(x)=\ln x$ 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 $x_{1} < x_{2}$, does there exist a real number $m$ such that $mg(x_{1})-mg(x_{2})-x_{2}f(x_{2})+x_{1}f(x_{1})$ is always positive? If it exists, find the range of $m$; if not, explain why.

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