
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 arithmetic sequence $\{a_{n}\}$ where all terms are positive, $a_{1}=3$. The sum of its first $n$ terms is denoted as $S_{n}$. Another sequence $\{b_{n}\}$ is a geometric sequence with $b_{1}=1$, and it satisfies $b_{2}S_{2}=64$, $b_{3}S_{3}=960$.

(I) Find the general terms of sequences $\{a_{n}\}$ and $\{b_{n}\}$;

(II) Calculate the sum: $\frac{1}{{S}_{1}}+\frac{1}{{S}_{2}}+...+\frac{1}{{S}_{n}}$.

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