
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 $A=\{x| -3 \leqslant x-2 \leqslant 1\}$, $B=\{x| a-1 \leqslant x \leqslant a+2\}$ $(a \in \mathbb{R})$.  
$(Ⅰ)$ When $a=1$, find $A \cap B$;  
$(Ⅱ)$ If $A \cup B = A$, find the range of real number $a$.

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