
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 $f(x)=ax-\frac{1}{x}-(a+1)\ln x, a\in R$.
(I) Find the monotonic intervals of the function $f(x)$ when the equation of the tangent line at $x=\frac{1}{2}$ is $4x-y+m=0$.
(II) Determine the number of zeros of the function $g(x)=x[f(x)+a+1]$ when $a>\frac{1}{e}$.

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