
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 the arithmetic sequence ${b_n}$ satisfies $(b_n + 2n = 2b_{n-1} + 4 (n=1,2,3,...))$, the sum of the first $n$ terms of the sequence ${a_n}$ is denoted as $S_n$, and $(S_n = 2^n - 1.(1))$. Find the general term formulas for ${a_n}$ and ${b_n}$; $(2)$ Let ${c_n = \frac{1}{b_n^2 - 1}}$, find the sum of the first $n$ terms of ${c_n}$, denoted as $T_n$.

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