
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
The function $f(x)=ax-\frac{a}{x}-2\ln x$ $(a\in\mathbb{R})$.

(Ⅰ) When $a=2$, find the equation of the tangent line to the curve $f(x)$ at $x=2$;

(Ⅱ) If $a > \frac{2e}{{e}^{2}+1}$, and $m$, $n$ are respectively the maximum and minimum values of $f(x)$, if $S=m-n$, find the range of $S$.

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