
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 universal set $U = \mathbb{R}$, set $A = \{x | 2 < x \leq 5\}$, $B = \{x | a - 1 < x < a + 1, a \in \mathbb{R}\}$.  
$(1)$ When $a = 2$, find $(\complement_{U}A) \cap (\complement_{U}B)$;  
$(2)$ If $x \in A$ is a necessary but not sufficient condition for $x \in B$, find the range of real numbers $a$.

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