
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 of the sequence $\{a\_n\}$ is $S\_n$, and $3S\_n = 4a\_n - 3n$, $n \in \mathbb{N}^*$,
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) The sequence $\{b\_n\}$ satisfies $\frac{b\_1}{1} + \frac{b\_2}{3} + \dots + \frac{b\_n}{2n-1} = \frac{a\_n}{3}$, $n \in \mathbb{N}^*$, find the general term formula of the sequence $\{b\_n\}$ and its sum of the first $n$ terms $T\_n$.

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