
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 two sets $A=\{x \mid -1 < x \leq 3\}$ and $B=\{x \mid m \leq x < 1 + 3m\}$,
(1) When $m=1$, find the union $A \cup B$;
(2) If $B \subseteq \bar{A}$, where $\bar{A}$ is the complement of $A$ with respect to the real number set, find the range of the real number $m$.

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