
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 $f(x) = \ln x - \frac{1}{2}a(x-1)$ ($a\in\mathbb{R}$).
- (Ⅰ) If $a = -2$, find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$.
- (Ⅱ) If the inequality $f(x) < 0$ holds for all $x \in (1, +\infty)$.
  - (i) Determine the range of the real number $a$.
  - (ii) Compare the magnitude of $e^{a-2}$ and $a^{e-2}$, and provide a proof ($e$ is the base of the natural logarithm, $e = 2.71828$).

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