
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 sequences ${a_n}$ and ${b_n}$ that satisfy $(a_{n+1} - a_n = 2(b_{n+1} - b_n))$, $n \in \mathbb{N_+}$, $(b_n = 2n - 1)$, and $(a_1 = 2)$.

(I) Find the general term formula for the sequence ${a_n}$;

(II) Let ${c_n = \frac{a_n^n}{b_n^{n-1}}}$, and let $T_n$ be the sum of the first $n$ terms of the sequence ${c_n}$. Find $T_n$.

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