
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 \(p: \left( \frac{x-4}{3} \right)^2 \leq 4\) and \(q: x^2 - 2x + 1 - m^2 \leq 0\) (\(m > 0\)). If the negation of \(p\) (\(\neg p\)) is a necessary but not sufficient condition for the negation of \(q\) (\(\neg q\)), find the range of values for the real number \(m\).

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