
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 $S\_n$, where $a\_1=8$ and $a\_n=3S_{n-1}+8$ for $n\geqslant 2$.

(1) Let $b\_n=\log \_2a\_n$, find the general formula for the sequence $\{b\_n\}$;
(2) Under the conditions in (1), let $c\_n=\frac{1}{b\_nb_{n+1}}$, find the first $n$ terms sum $T\_n$ of the sequence $\{c\_n\}$.

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