
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 $p$: $-2 \leq \frac{4-x}{3} \leq 2$, and $q$: $x^2 - 2x + 1 - m^2 \leq 0$ ($m > 0$), 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}
user