
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 $A={x|1-m\leqslant x\leqslant 2m+1}$ and $B={x|\frac{1}{9}\leqslant {3}^{x}\leqslant 81}$.

(1) Find $A\cup B$ when $m=2$;

(2) Find the range of real number $m$ if $B\subseteq A$.

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