
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 a sequence $\{a\_n\}$ where all terms are positive, let $S\_n$ denote the sum of its first $n$ terms. For any $n \in \mathbb{N}^*$, it is known that $a\_n, S\_n, a\_n^{2}$ form an arithmetic sequence.

(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Find the sum of the first $n$ terms of the sequence $\{\frac{2}{a\_n \cdot a\_{n+1}}\}$.

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