
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
Let $A=\{x | -1 \lt x \lt 3\}$, $B=\{x | 2-a \lt x \lt 2+a\}$.  
$(1)$ If $a=2$, find $A\cup B$ and $A\cap B$;  
$(2)$ Let proposition $p:x\in A$, proposition $q:x\in B$. If $p$ is a necessary but not sufficient condition for $q$ to hold, find the range of real number $a$.

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