
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 the sum of the first $n$ terms of a positive arithmetic sequence ${a_n}$ is ${S_n}$, if $S_3=12$, and ${a_1}$, ${a_2}$, ${a_3}+2$ form a geometric sequence.

(I) Find the general term formula for ${a_n}$;

(II) If ${b_n}={3^n}{a_n}$, the sum of the first $n$ terms of the sequence ${{b_n}}$ is ${T_n}$, find ${T_n}$.

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