
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 the sets $A=\left\{ x \mid 0 < x-m < 3\right\}$ and $B=\left\{ x \mid x\leqslant 0 \text{ or } x\geqslant 3 \right\}$,

(1) Find $A \cap B$ when $m=1$.
(2) Find the range of $m$ when $A \cup B = B$.

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