
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
Definition: The difference between the maximum and minimum values of the function $f(x)$ in the interval $[a,b]$ is called the range of $f(x)$ in the interval $[a,b]$, denoted as $d(a,b)$.  
$(1)$ If $f(x)=x^{2}-2x+2$, then $d(1,2)=$ \_\_\_\_\_\_ ；  
$(2)$ If $f(x)=x+ \frac {m}{x}$, and $d(1,2)\neq |f(2)-f(1)|$, then the range of the real number $m$ is \_\_\_\_\_\_ ．

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