
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 $P=\left\{{x|\frac{4}{{x+2}}≥1}\right\}$, and the non-empty set $S=\{x\left|\right.1-m\leqslant x\leqslant 1+m\}$.<br/>$(1)$ When $m=2$, find $P\cup S$;<br/>$(2)$ If $x\in P$ is a necessary condition for $x\in S$, find the range of real number $m$.

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