
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 sets $A=\{x| -1\leqslant x\leqslant 2\}$, $B=\{x| (x-a)(x-a-1) \lt 0\}$, $a\in R$.  
$(1)$ If $1\in B$, find the range of real number $a$;  
$(2)$ If "$x\in B$" is a sufficient but not necessary condition for "$x\in A$", find the range of real number $a$.

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