
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 terms in the arithmetic sequence $\{a_n\}$ are all positive with $a_1 = 3$. The sum of the first $n$ terms is denoted as $S_n$. $\{b_n\}$ is a geometric sequence with $b_1 = 2$. It is given that $b_2S_2 = 32$ and $b_3S_3 = 120$.

(1) Find $a_n$ and $b_n$;
(2) Find the sum of the first $n$ terms of the sequence $\{a_nb_n\}$, denoted as $T_n$.

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