
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 $\{a_n\}$ is a monotonically increasing arithmetic sequence with the first term $a_1=3$, and the sum of the first $n$ terms is $S_n$. The geometric sequence $\{b_n\}$ has the first term $b_1=1$, and it is given that $a_2b_2=12$ and $S_3+b_2=20$.

(1) Find the general formula for $\{a_n\}$ 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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