
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 increasing geometric sequence $\{a_{n}\}$ and the arithmetic sequence $\{b_{n}\}$, such that $(a_{1}+a_{4}=18, a_{2}a_{3}=32)$, $b_{2}$ is the arithmetic mean of $a_{1}$ and $a_{2}$, and $(b_{3}=a_{3}-3)$.

(I) Find the general term formula for the sequences $\{a_{n}\}$ and $\{b_{n}\}$.

(II) If $\frac{1}{c_{n}}= \frac{1}{b_{n}b_{n+1}}$, find the sum of the first $n$ terms $(S_{n})$ of the sequence $\{c_{n}\}$.

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