
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 $2a_5$, $a_4$, $4a_6$ form an arithmetic sequence, satisfying $a_4=4a_3^2$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) Let $b_n= \frac {a_{n+1}}{(1-a_n)(1-a_{n+1})}$, $n\in\mathbb{N}^*$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, $S_n$.

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