
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: The real number $x$ satisfies $$x^{2}-2x-8\leq C_{n}^{0} - C_{n}^{1} + C_{n}^{2} - C_{n}^{3} + \ldots + (-1)^{n}C_{n}^{n}$$; proposition q: The real number $x$ satisfies $|x-2|\leq m$ ($m>0$).
(1) When $m=3$, if "p and q" is true, find the range of real numbers $x$.
(2) If "not p" is a necessary but not sufficient condition for "not q", find the range of real numbers $m$.

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