
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 proposition $P:\{x|\left\{\begin{array}{l}{x+2≥0}\\{x-10≤0}\end{array}\right.\}$, proposition $q:\{x\left|\right.1-m\leqslant x\leqslant 1+m,m \gt 0\}$.  
$(1)$ If $m=1$, what is the condition for $p$ to be $q$?  
$(2)$ If $p$ is a necessary but not sufficient condition for $q$, find the range of real number $m$.

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