
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 ${a_n}$ satisfies $(a_{1}+a_{2})+(a_{2}+a_{3})+…+(a_{n}+a_{n+1})=2n(n+1) (n∈N^{*})$.
(1) Find the general term formula for the sequence ${a_n}$;
(2) In sequence ${b_n}$, $b_{1}$=1, $b_{2}$=2. If we take the $b_{n}^{th}$ term from sequence ${a_n}$ and denote it as $c_{n}$, and ${c_n}$ is a geometric sequence, find the sum of the first $n$ terms of ${b_n}$, denoted as $T_{n}$.

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