
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
In a non-zero common difference arithmetic sequence $\{a\_n\}$, $a\_3 + a\_{10} = 15$, and $a\_2$, $a\_5$, $a\_{11}$ form a geometric sequence.

1. Find the general term formula for $\{a\_n\}$.
2. Let $b\_n = \frac{1}{a\_n a\__{n+1}}$, find the sum of the first $n$ terms, $S\_n$, of the sequence $\{b\_n\}$.

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