
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 an arithmetic sequence $\{a\_n\}$ with a non-zero common difference $d$, the sum of the first 7 terms $S\_7 = 35$, and the terms $a\_2$, $a\_5$, $a\_11$ form a geometric sequence.

(1) Find the general term formula for the sequence $\{a\_n\}$.
(2) Find the sum of the first $n$ terms, denoted as $T\_n$, for the sequence $\{\frac{1}{a\_n a\_{n+1}}\}$.

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