
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 $m > 0$, $p:(x+2)(x-6)\leqslant 0$, $q:2-m\leqslant x\leqslant 2+m$.

$(1)$ If $p$ is a sufficient condition for $q$, find the range of the real number $m$;

$(2)$ If $m=5$, "either $p$ or $q$" is true, and "both $p$ and $q$" is false, find the range of the real number.

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