
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 $\{a_n\}$ with its first $n$ terms sum $S_n$, and for any positive integer $n$, $a_n=\frac{3}{4}S_n+2$ holds.

(I) Let $b_n=\log_2 a_n$, find the general term formula of the sequence $\{b_n\}$.

(II) Let $c_n=\frac{1}{b_nb_{n+1}}$, find the sum of the first $n$ terms $T_n$ of the sequence $\{c_n\}$.

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