
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 $A = \{x|1-m \leq x \leq 2m+1\}$, $B = \{x| \frac{1}{9} \leq 3^{x} \leq 81\}$:
1. When $m=2$, find $A \cup B$;
2. If $B \subseteq A$, find the range of the real number $m$.

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