
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
(1) If $(-a^2b^m)^3 = -a^nb^{12}$, then $m=\ $, $n=\ $;  
(2) Given that $2^{2x+2} - 2^{2x+1} = 32$, find the value of $x$.

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