
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
In the arithmetic sequence $\{a_n\}$, $a_2 + a_3 = -2$ and $a_4 + a_5 + a_6 = 12$. Let $S_n$ be the sum of the first $n$ terms of $\{a_n\}$.
1. Find the general term $a_n$ and the sum $S_n$.
2. Given that ${b_n - a_n}$ is a geometric sequence with the first term 1 and common ratio 3, determine the general formula for the terms of the sequence $\{b_n\}$ and the sum of its first $n$ terms, $T_n$.

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