
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
If $A=\{x|1＜{(\frac{1}{2})}^{x-a}＜4\}$, $B=\{x|\frac{1}{2-x}≤1\}$,  
$(1)$ When $a=\frac{3}{2}$, find $A∩\overline{B}$;  
$(2)$ If $x\in A$ is a sufficient condition for $x\in B$, find the range of real number $a$.

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