
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 the sequence $\{a\_n\}$, where $n \in \mathbb{N}^+$, is an arithmetic sequence with a non-zero common difference. If $a\_1 = 1$ and $a\_2$, $a\_4$, $a\_8$ form a geometric sequence:

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

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