
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 set $A=\{x|x^{2}-4x-12\leqslant 0\}$, set $B=\{x|x^{2}-mx-6m^{2}\leqslant 0\ (m \gt 0)\}$.  
$(1)$ Find sets $A$ and $B$;  
$(2)$ If $x\in A$ is a condition for $x\in B$ to hold, choose one from the options of ① sufficient but not necessary, ② necessary but not sufficient, ③ sufficient, ④ necessary to supplement in question (2), to determine if there exists a real number $m$, and if it exists, find the range of values for $m$, if not, explain the reason.

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