
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 of positive terms $\{a_n\}$, the sum of the first $n$ terms is $S_n$. When $n\geqslant 2$, $(a_n-S_{n-1})^{2}=S_{n}S_{n-1}$, and $a_1=1$. Let $b_n=\log_{2} \frac {a_{n+1}}{6}$, determine the value of $b_n$.

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