
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 $f(x)=2ax+bx-1-2\ln x(a∈R)$,

(1) Discuss the monotonic intervals of the function $f(x)$ when $b=0$;

(2) When $a=1$, if $\forall x\in (0,+\infty ),f(x)\geqslant 2bx-3$ always holds, find the range of values of the real number $b$.

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