
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: \\
- $p$: $|x+1| \leqslant 3$,
- $q$: $x^2 - 2x + 1 - m^2 \leqslant 0$,
- $m > 0$.

(I) If $m=2$, for the proposition "$p$ or $q$" to be true and "$p$ and $q$" to be false, find the range of real numbers $x$.

(II) If $p$ is a necessary but not sufficient condition for $q$, find the range of real numbers $m$.

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