
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 set $A=\{x\mid 1-m\leq x \leq 2m+1\}$ and $B=\left\{x\mid \frac{1}{9}\leq 3^x \leq 81\right\}$.
(1) When $m=2$, find $A\cap B$ and $A\cup B$;
(2) If $B \subseteq A$, find the range of the real number $m$.

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