
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 a sequence $\{a\_n\}$ where the sum of its first $n$ terms is $S\_n$, and $S\_n = \frac{4}{3}(a\_n - 1)$, find the minimum value of $(4^{n-2} + 1)(\frac{16}{a\_n} + 1)$.

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