
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 an arithmetic sequence $\{a_n\}$, where $a_1=3$, and the sum of its first $n$ terms is $S_n$. For a geometric sequence $\{b_n\}$ with positive terms, where $b_1=1$, the common ratio is $q$, and it's known that $b_2 + S_2 = 12$ and $q=\frac{S_2}{b_2}$.
(I) Find the formulas for $a_n$ and $b_n$.
(II) Let $T_n = a_n b_1 + a_{n-1} b_2 + \ldots + a_1 b_n$ for $n \in \mathbb{N}^+$. Find the value of $T_n$.

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