
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 first term ${a_1=3}$, and the sum of its first $n$ terms is ${S_n}$. The geometric sequence ${b_n}$ has first term ${b_1=1}$, and it is known that ${a_2b_2=12}$, ${S_3+b_2=20}$.

(I) Find the general terms of ${a_n}$ and ${b_n}$;
(II) Find the sum of the first $n$ terms of ${a_nb_n}$, denoted as ${T_n}$.

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