
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 $A=\{x|x^{2}-5x+4\leqslant 0\}$ and $B=\{x\left|\right.2-m\leqslant x\leqslant 2+m\}$.  
$(1)$ If $A\cap B=B$, find the range of real number $m$;  
$(2)$ Let $p:x\in A$, $q:x\in B$. If $q$ is a necessary but not sufficient condition for $p$, find the range of real number $m$.

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