
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 $f(x) = \frac{\ln x + 1}{x}$,

(1) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(e, f(e))$;

(2) When $x \geqslant 1$, the inequality $f(x) - \frac{1}{x} \geqslant \frac{a(x^2 - 1)}{x}$ always holds. Find the range of values for $a$.

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