
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
The terms of an arithmetic sequence $\\{a_{n}\\}$ are all positive numbers, with $a_{1}=3$. The sum of the first $n$ terms is denoted by $S_{n}$. The sequence $\\{b_{n}\\}$ is a geometric sequence with $b_{1}=1$, and it satisfies the equations $b_{2}S_{2}=64$ and $b_{3}S_{3}=960$.

1. Find the expressions for $a_{n}$ and $b_{n}$.
2. Compute 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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