
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 $S_{n}$ is the sum of the first $n$ terms of the sequence ${a_{n}}$, and it satisfies $S_{n}= \frac {1}{2}n^{2}+ \frac {3}{2}n$. The sum of the first $n$ terms of the positive geometric sequence ${b_{n}}$ is $T_{n}$, and it satisfies $b_{3}=8$, $T_{2}=6$.
(I) Find the general term formulas for the sequences ${a_{n}}$ and ${b_{n}}$;
(II) Let $c_{n}=a_{n} \cdot b_{n},n\in\mathbb{N}^{*}$, find the sum of the first $n$ terms of the sequence ${c_{n}}$, denoted as $G_{n}$.

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