
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 set $A=\{x|x^{2} < 9, x \in \mathbb{Z}\}$, $B=\{x|2x > a\}$.  
$(1)$ If $a=1$, list all proper subsets of $A \cap B$;  
$(2)$ If $A \cap B$ has $4$ subsets, find the range of values for $a$.

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