
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 that the sequence $\{a\_n\}$ is an arithmetic sequence, $a\_1=1$, $a\_n > 0$, and the sum of its first $n$ terms is $S\_n$. Also, the sequence $\{ \sqrt{S\_n} \}$ is an arithmetic sequence.

(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Let $b\_n=\frac{a_{n+1}}{S\_n \cdot S_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$.

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