
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 that the sum of the first $n$ terms, $S_{n}$, of a sequence ${a_{n}}$ satisfies the equation $2S_{n}=3a_{n-1}$, where $n\in\mathbb{N}^*$.

(1) Find the general term formula for the sequence ${a_{n}}$.

(2) If $a_{n}b_{n}=\frac{3^{n}}{n^{2}+n}$, find the sum of the first $n$ terms, $T_{n}$, for the sequence ${b_{n}}$.

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