
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 $f(x)=|ax-2|+b\ln x(x > 0)$, where $a$ and $b$ are constants.
(1) If $a=1$, find the range of $b$ such that $f(x)$ is a monotonically increasing function on $(0,+\infty)$;
(2) If $a\geqslant 2$, $b=1$, find the number of solutions to the equation $f(x)= \frac {1}{x}$ on $(0,1]$.

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