
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 geometric sequence $\{a_n\}$ satisfies $a_1a_2a_3=8$ and $a_5=16$.

(Ⅰ) Find the general formula for $\{a_n\}$ and the sum of the first $n$ terms $S_n$;

(Ⅱ) Let $b_n=\log_2a_{n+1}$, find the sum of the first $n$ terms $T_n$ for the sequence $\left\{ \frac{1}{b_nb_{n+1}} \right\}$.

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