
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 $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, and for any positive integer $n$ the following relationship holds: $a_n = \frac{3}{4}S_n + 2$. If $b_n = \log_2 {a_n}$, then find the value of $b_{1008}$.

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