
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 $f(x)$ satisfies $f\left(\log_a x\right) = \frac{a}{a^2-1}\left(x - x^{-1}\right)$ where $a > 0$, $a \neq 1$

(Ⅰ) Find the expression for $f(x)$;

(Ⅱ) For the function $f(x)$, when $x \in (-1,1)$, $f(1-m)+f(1-m^2) < 0$, find the range of the real number $m$;

(Ⅲ) When $x \in (-\infty,2)$, the value of $f(x)-4$ is negative, find the range of $a$．

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