
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 $$A=\{x| \frac {1}{32} \leq 2^{-x} \leq 4\}$$, and $B=\{x|x^2-3mx+2m^2-m-1<0\}$.  
(1) When $x \in \mathbb{Z}$, find the number of non-empty proper subsets of $A$.  
(2) If $B=\emptyset$, find the range of values for $m$.  
(3) If $A \supseteq B$, find the range of values for $m$.

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