
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 $2^m = 8$, and $2^n = 32$, then $2^{2m+n-4} =$ ?  
(2) If $x = 2^m - 1$, express $y = 1 + 4^{m+1}$ in terms of $x$.

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