
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 $p$: $-x^2+6x+16\geq0$, $q$: $x^2-4x+4-m^2\leq0$ ($m>0$).
1. If $p$ is true, find the range of real numbers $x$.
2. If $p$ is a sufficient but not necessary condition for $q$, find the range of real numbers $m$.

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