
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 a set $A$ with three elements: $a-3$, $2a-1$, $a^{2}+1$, and a set $B$ with three elements: $0$, $1$, $x$.  
$(1)$ If $-3 \in A$, find the value of the real number $a$;  
$(2)$ If $x^{2} \in B$, find the value of the real number $x$.

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