
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 $h(x)=ax (a\in R)$.
(I) Find the range of values for the real number $a$ such that the graphs of functions $f(x)$ and $h(x)$ have no common points.
(II) Determine whether there exists a real number $m$ such that for any $x\in (\frac{1}{2},+\infty)$, the graph of the function $y=f(x)+\frac{m}{x}$ is always below the graph of $g(x)=\frac{e^{x}}{x}$. If such an $m$ exists, find the maximum integer value of $m$; otherwise, provide a reason.
(Reference data: $\ln 2=0.6931$, $\ln 3=1.0986$, $\sqrt{e}=1.6487$, $\sqrt[3]{e}=1.3956$)

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