
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 the sequence $\{a_n\}$ satisfies: $a_1+3a_2+3^2a_3+…+3^{n-1}a_n=\frac{n+1}{3}$, $(n\in \mathbb{N}^*)$

(I) Find the general formula for the sequence $\{a_n\}$;

(II) Let $b_n=\frac{1}{3^{n+1}(1-a_n)(1-a_{n+1})}$, the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n$, try to compare the size of $S_n$ and $\frac{7}{16}$

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