
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 $f(x)= \frac {a}{x}-\ln x$ ($a\in\mathbb{R}$)  
(I) If the graph of $f(x)$ is tangent to the line $y=0$, find $a$.  
(II) If $e+1 < a < e^{2}$ and the zero of the function $f(x)= \frac {a}{x}-\ln x$ is $x_{0}$,  
let the function $g(x)= \begin{cases} \frac {a}{x}-\ln x- \frac {\ln x}{x}, & 0 < x < x_{0} \\ \ln x- \frac {a}{x}- \frac {\ln x}{x}, & x > x_{0}\end{cases}$. Discuss the number of zeros of the function $g(x)$. ($e\approx2.71828$ is the natural constant)

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