
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 the sequence ${a_n}$ is $S_n$, and vectors $\overrightarrow{a} = (S_n, 1)$ and $\overrightarrow{b} = (2^n - 1, \frac{1}{2})$ satisfy the condition $\overrightarrow{a} \parallel \overrightarrow{b}$.
1. Find the general term formula for the sequence ${a_n}$.
2. The sequence ${b_n}$ satisfies $b_1 = 1$ and $b_{n+1} - b_n = 1$. If $c_n = \frac{b_n}{a_n}$, find the sum of the first $n$ terms of the sequence ${c_n}$, denoted as $T_n$.

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