
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 $S_n=n(n+1)+2$, where $n\in\mathbb{N}^*$.
(I) Find the general term formula of the sequence ${a_n}$;
(II) If $a_2$, $a_{k+2}$, $a_{3k+2}$ ($k\in\mathbb{N}^*$) are the first three terms of the geometric sequence ${b_n}$, find the general term formula of the sequence ${b_n}$.

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