
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
In the arithmetic sequence $\{a_n\}$, $a_1=3$, and the sum of the first $n$ terms is $S_n$. In the geometric sequence $\{b_n\}$, all terms are positive, $b_1=1$, and $b_2+S_2=12$. The common ratio of $\{b_n\}$ is given by $q=\frac{S_2}{b_2}$.

1. Find $a_n$ and $b_n$.
2. Find $T_n=S_{b_1}+S_{b_2}+S_{b_3}+S_{b_4}+\dots+S_{b_n}$.

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