
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 positive sequence $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$, for $n \geq 2$, $(a_n - S_{n-1})^2 = S_n S_{n-1}$, and $a_1 = 1$, express $b_n$ in terms of $n$ where $b_n = \log_2 \frac{a_{n+1}}{6}$.

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