
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 the universal set be $U = \mathbb{R}$, set $A = \{x | 1 \leq x \leq 5\}$, set $B = \{x | -1-2a \leq x \leq a-2\}$.  
$(1)$ If "$x \in A$" is a sufficient but not necessary condition for "$x \in B$", find the range of real number $a$;  
$(2)$ If $B \subseteq A$, find the range of real number $a$.

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