
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 $f(x)=\ln x-ax+\frac{1-a}{x}-1$,
(1) Discuss the monotonicity of the function $f(x)$ when $a < \frac{1}{2}$;
(2) Let $g(x)=x^{2}-2bx+\frac{4}{3}$, when $a=\frac{1}{3}$, if for any $x\_1\in(0,2)$, there exists $x\_2\in[1,3]$, 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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