
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 $\rho$: $\left|1- \frac{x-1}{3}\right| \leq 2$, $q$: $(x-1+m)(x-1-m) \leq 0$ ($m > 0$), if $q$ is a sufficient but not necessary condition for $p$, find the range of the real number $m$.

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