
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 $A=\{x|x-a)(x-a+1)\leqslant 0\}$, $B=\{x|x^{2}+x-2 \lt 0\}$.  
$(1)$ If $x\in A$ is a sufficient but not necessary condition for $x\in B$, find the range of real number $a$.  
$(2)$ Let proposition $p:\exists x\in B$, $x^{2}+(2m+1)x+m^{2}-m \gt 8$. If proposition $p$ is false, find the range of real number $m$.

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