
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 the set $A=\{x|x^{2}+3x-10\leqslant 0\}$  
$(1)$ If the set $B=[-2m+1,-m-1]$, and $A\cup B=A$, find the range of the real number $m$;  
$(2)$ If the set $B=\{x|-2m+1\leqslant x\leqslant -m-1\}$, and $A\cup B=A$, find the range of the real number $m$.

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