
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 $f(x) = \frac{1}{x} - a\ln x$ ($a \in \mathbb{R}$)，  
(I) When $a = -1$,  
(i) Find the equation of the tangent line to $f(x)$ at the point $(1, f(1))$,  
(ii) Let $g(x) = xf(x) - 1$, find the extreme values of the function $g(x)$,  
(II) If the function $f(x)$ has two distinct zeros in the interval $\left[\frac{1}{e^2}, +\infty\right)$, find the range of the real number $a$.

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