
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 $f(x) = \frac{1}{x-1} - \frac{2}{\sqrt{x-1}} + 2$.

(Ⅰ) Find the domain of the function $f(x)$.

(Ⅱ) If $g(x) = f\left(\frac{1+x^2}{x^2}\right)$, ($x \neq 0$), find the expression and the minimum value of $g(x)$.

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