
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]


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(1) The solution set of the inequality $\dfrac{x-1}{x} < 2$ with respect to $x$ is ______.

(2) The value of ${{\left(\dfrac{16}{81}\right)}^{-\frac{3}{4}}}+{{\log }_{3}}\dfrac{5}{4}+{{\log }_{3}}\dfrac{4}{5}=$ ______.

(3) Given $f\left( 1-{\cos }x \right)={\sin}^{2}x$, the expression for $f\left( {{x}^{2}} \right)$ is ______.

(4) If $x\in (-\infty ,-1]$, the inequality $(m-{m}^{2}){{4}^{x}}+{{2}^{x}}+1 > 0$ always holds, then the range of the real number $m$ is ______.

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