
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 geometric sequence ${a_n}$ with a common ratio $q>1$, $a_2$ and $a_3$ are the two roots of the equation $x^2-6x+8=0$.
(1) Find the general term formula for the sequence ${a_n}$;
(2) Find the sum of the first $n$ terms, $S_n$, for the sequence ${2n \cdot a_n}$.

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