
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 $A=\{x\left|\right.-1\leqslant x\leqslant 2\}$ and $B=\{x|x^{2}-2mx+m^{2}-1\leqslant 0\}$.  
$(1)$ Let proposition $p:x\in A$, proposition $q:x\in B$, and $p$ is a necessary but not sufficient condition for $q$. Find the range of real number $m$.  
$(2)$ If for all $x\in A$, $x^{2}+m\geqslant 4+3x$, find the range of real number $m$.

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