
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 $f(x)= \frac {2x^{2}}{e}+ \frac {e^{2}}{x}$, $g(x)=3e\ln x$, where $e$ is the base of the natural logarithm.
- (I) Discuss the monotonicity of the function $f(x)$.
- (II) Determine whether the curve $y=f(x)$ and $y=g(x)$ have a common point and a common tangent line at that point. If such a point exists, find the equation of the common tangent line $l$; if not, explain why.

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