
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 an arithmetic sequence ${a_n}$ with $a_n > 0$, its sum of the first $n$ terms is $S_n$. If $S_3 = 12$ and $2a_1, a_2, a_3 + 1$ form a geometric sequence, find:
1. The general term formula for ${a_n}$
2. The sum $T_n$ of the first $n$ terms of the sequence ${b_n} = a_n \cdot 3^n$

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