
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 non-zero common difference arithmetic sequence $\{a\_n\}$, it satisfies $a\_1+a\_3+a\_5=9$, and $a\_1$, $a\_4$, $a\_16$ form a geometric sequence.

(1) Find the general term formula of the sequence $\{a\_n\}$;

(2) Let $b\_n=\frac{1}{a\_n a\_{n+1} a\_{n+2}}$, find the sum of the first $n$ terms $S\_n$ of the sequence $\{b\_n\}$.

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