
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 $A = \{x | 0 < 2x + a \leq 3\}$, $B = \left\{x | -\frac{1}{2} < x < 2\right\}$.  
$(1)$ When $a = 1$, find $(\complement_{U}B) \cup A$;  
$(2)$ If $A \subseteq B$, find the range of real number $a$.

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