
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: A real number $x$ satisfies $(x^2+1)(x^2-8x-20) \leq 0$, and proposition q: A real number $x$ satisfies $x^2-2x+(1-m^2) \leq 0$ ($m > 0$). If $\neg p$ is a necessary but not sufficient condition for $\neg q$, find the range of the real number $m$.

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