
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
Consider two sequences, an arithmetic sequence $\{a\_n\}$ with all positive terms and $a\_1=1$, and its partial sum $S\_n$, and a geometric sequence $\{b\_n\}$ with $b\_1=1$. Given that $b\_2S\_2=6$ and $b\_2+S\_3=8$.

1. Find the general term formulas for both $\{a\_n\}$ and $\{b\_n\}$.
2. Compute the sum $\frac{1}{S\_1}+\frac{1}{S\_2}+\cdots+\frac{1}{S\_n}$.

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