
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 an geometric sequence $\{a_{n}\}$ with the sum of the first $n$ terms denoted as $S_{n}$. It is known that $a_{3}=\frac{1}{8}$, and the sequence formed by $S_{2}+\frac{1}{16}$, $S_{3}$, $S_{4}$ is an arithmetic sequence. Additionally, the sequence $\{b_{n}\}$ satisfies $b_{n}=8n$.

(I) Find the general term formula for the sequence $\{a_{n}\}$;

(II) Find the sum of the first $n$ terms, $T_{n}$, for the sequence $\{a_{n}\cdot b_{n}\}$.

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