
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 $f(x)=ax- \frac {a}{x}-2\ln x$ $(a > 0)$  
(I) When $a=2$, find the number of zeros of the function $f(x)$;  
(II) Discuss the monotonicity of $f(x)$;  
(III) Let the function $g(x)= \frac {2e}{x}$, if there exists at least one point $x_{0}$ in $[1,e]$ such that $f(x_{0}) > g(x_{0})$ holds, find the range of the real number $a$.

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