
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 $f(x)=px- \frac {p}{x}-2\ln x$.
- (I) If $p=2$, find the equation of the tangent line to the curve $f(x)$ at the point $(1,f(1))$;
- (II) If the function $f(x)$ is increasing in its domain, find the range of the positive real number $p$;
- (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 $p$.

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