
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 ${S_{n}}$ be the sum of the first $n$ terms of the sequence ${{a_{n}}}$, with ${{a_{1}}=3}$ and ${{a_{n+1}}=2{{S_{n}}+3}}$, for all $n\in \mathbb{N}^*$.

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

(2) Let ${{b_{n}}=(2n-1){{a_{n}}}}$. Find the sum ${{T_{n}}}$ of the first $n$ terms of the sequence ${{b_{n}}}$.

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