
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
A sequence ${a_{n}}$ is a geometric sequence where $a_{1}=1$, $a_{4}=8$. If $a_{3}$, $a_{5}$ are the 4th and 16th terms respectively of an arithmetic sequence ${b_{n}}$.
(1) Find the general term formulas for both sequences ${a_{n}}$ and ${b_{n}}$;
(2) Let ${c_{n}} = a_{n} \cdot b_{n}$, find the sum of the first $n$ terms $S_{n}$ for the sequence ${c_{n}}$.

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