
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
Let the sequence $\{a_n\}$, where each term is positive, have a sum of the first $n$ terms denoted by $S_n$, and $S_n$ satisfies $2S_n^2-(3n^2+3n-2)S_n-3(n^2+n)=0$, where $n\in\mathbb{N}^*$.  
(Ⅰ) Find the value of $a_1$;  
(Ⅱ) Find the general formula for the sequence $\{a_n\}$;  
(Ⅲ) Let $b_n= \frac {a_n}{3^{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted by $T_n$.

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