
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 $f(x)=x+ \frac {b}{x}-3$, where $x\in[1,2]$,
(1) Find the range of $f(x)$ when $b=1$;
(2) If $b\geqslant 2$, the maximum value of $f(x)$ is $M$, and the minimum value is $m$, such that $M-m\geqslant 4$, find the range of $b$.

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