
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
Let the set $A = \left\{ x\middle| \frac{1}{4} \leq 2^x \leq 32\right\}$, and the set $B = \left\{ x\middle|x^2 - 3mx + (2m+1)(m-1) < 0 \right\}$.
(1) If $m > 2$ and $A \cap B \neq \emptyset$, find the range of values for $m$;
(2) If $B \subseteq A$, find the range of values for $m$.

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