
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 sets $A=\{x|x^{2}-2x-8\leqslant 0\}$ and $B=\{x|x^{2}-2x+1-m^{2}\leqslant 0, m \gt 0\}$.  
$(1)$ If $m=2$, find $A$⋂$(\complement _{R}B)$;  
$(2) x\in A$ is a ____ condition for $x\in B$, find the range of $m$. (Please choose one from "① sufficient but not necessary; ② necessary but not sufficient" and fill in the blank) Note: If multiple conditions are chosen for separate answers, score according to the first answer.

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