
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 $p$: $4x^{2}+12x-7\leqslant 0$, $q$: $a-3\leqslant x\leqslant a+3$.  
$(1)$ When $a=0$, if $p$ is true and $q$ is false, find the range of real numbers $x$;  
$(2)$ If $p$ is a sufficient condition for $q$, find the range of real numbers $a$.

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