
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 a sequence ${a_n}$ with its first $n$ terms sum $S_n$, where $S_n = 2a_n - a_1$, and $a_1 - 1, a_2 - 1, a_3 - 3$ are the first three terms of an arithmetic sequence ${b_n}$.
1. Find the general term formula for the sequences ${a_n}$ and ${b_n}$.
2. Let $c_n = a_n + b_n, n \in \mathbb{N}^*$, find the sum of the first $n$ terms, $T_n$, for the sequence ${c_n}$.

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