
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 \( p: \left|1-\frac{x-1}{3}\right| \leqslant 2 \) and \( q: x^2 - 2x + 1 - m^2 \leqslant 0 (m > 0) \), \(\neg p\) is a necessary but not sufficient condition for \(\neg q\). Determine the range of the real number \( m \).

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