
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 $f(x)= \dfrac {x+a}{x+b}$ (where $a,b$ are constants),  
$(1)$ If $b=1$, solve the inequality $f(x-1) > 0$;  
$(2)$ When $x∈[-1,2]$, the range of $f(x)$ is $[\dfrac {5}{4},2]$, find the values of $a$ and $b$.

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