
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
The terms of the geometric sequence $\{a_n\}$ are all positive, and $2a_3$ is the geometric mean of $a_2$ and $a_6$, $2a_1+3a_2=16$.

(Ⅰ) Find the general formula for the sequence $\{a_n\}$;  
(Ⅱ) Let $b_n=\log_2a_1+\log_2a_2+\ldots+\log_2a_n$, find the sum of the first $n$ terms $S_n$ of the sequence $\left\{ \frac{1}{b_n} \right\}$.

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