
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 $f(x)=x\ln x$, $g(x)=-x^{2}+ax-2$ ($e\approx2.71$, $a\in\mathbb{R}$).  
(I) Determine the number of common points between the tangent line of the curve $y=f(x)$ at the point $(1,f(1))$ and the curve $y=g(x)$.  
(II) When $x\in\left[\frac{1}{e},e\right]$, if the function $y=f(x)-g(x)$ has two zeros, find the range of values for $a$.

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