
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 function $f(x)=4^{x}$, the point $(a_{n},b_{n})$ lies on the graph of the function $y=f(x)$. Let $S_{n}$ be the product of the first $n$ terms of the sequence ${b_{n}}$, and $S_{n}=2^{n(n+1)}$.

(1) Find the general term formulas for the sequences ${a_{n}}$ and ${b_{n}}$.
(2) Let $c_{n}= \frac{1}{a_{n+1} \cdot \log_{4}b_{n}}$, find the sum of the first $n$ terms of the sequence ${c_{n}}$.

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