
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 $f(x)=ax-1-\ln x$ $(a\in\mathbb{R})$.
- (I) Discuss the number of extreme points of the function $f(x)$ within its domain.
- (II) If $a=1$, for all $x\in(0,+\infty)$, $f(x)\geqslant bx-2$ always holds, find the range of the real number $b$.

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