
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 function $f(x)=a\ln x+2a$, $g(x)=x+ \frac {a}{x}$ (where $a$ is a constant, $a\in\mathbb{R}$).  
(I) Find the monotonic intervals of the function $g(x)$.  
(II) When $a > 0$, does there exist a real number $a$ such that for any $x_{1}$, $x_{2}\in[1,e]$ the inequality $f(x_{1})-g(x_{2}) > 0$ always holds? If it exists, find the range of $a$; if not, explain why (where $e$ is the base of the natural logarithm, $e=2.71828…$)

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