
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 $f(x)=x+ \frac{4a}{x}-1$, $g(x)=a\ln x$, $a\in R$.
(I) If the function $h(x)=f(x)-g(x)$ is a decreasing function on $[1,3]$, find the minimum value of $a$;
(II) If the function $p(x)=(2-x^{3})\cdot e^{x}$ ($e=2.718...$, $e$ is the base of the natural logarithm), $q(x)= \frac{g(x)}{x}+2$, for any $x_{1}$, $x_{2}\in(0,1)$, $p(x_{1}) > q(x_{2})$ always holds, find the range of $a$.

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