
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 $f(x)=\ln x-ax+\frac{1-a}{x}-1$, where $a\in R$

(1) Discuss the monotonicity of $f(x)$;

(2) Let $g(x)={x}^{2}-2bx+4$, when $a=\frac{1}{4}$, if for $\forall {{x}\_{1}}\in (0,2), \exists {{x}\_{2}}\in \[1,2\]$, such that $f({{x}\_{1}})\geqslant g({{x}\_{2}})$, find the range of values for the real number $b$.

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