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

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