
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 $f(x)=ax-\frac{1}{x}-(a+1)\ln x$, where $a\in R$.
(I) If $a=-2$, find the monotonic intervals of the function $f(x)$;
(II) If $a\geqslant 1$, and $f(x) > 1$ holds true in the interval $[\frac{1}{e},e]$, find the range of values for $a$;
(III) If $a > \frac{1}{e}$, determine the number of zeros of the function $g(x)=x[f(x)+a+1]$.

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