
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 sequence ${a_n}$ has a sum of its first $n$ terms denoted as $S_n$, with $a_1=2$ and $S_n=\frac{3}{2}a_n-1$ for all $n\in\mathbb{N}^*$.
(1) Find the general formula for the $n$-th term of the sequence.
(2) Let $b_n=n\cdot a_n$, find the sum of the first $n$ terms of the sequence ${b_n}$, denoted as $T_n$.

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