
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 common difference $d \neq 0$, it is known that $a_{1} + a_{4} = 14$, and $a_{1}$, $a_{2}$, $a_{7}$ form a geometric sequence.

(1) Find the general term formula $a_{n}$ and the sum formula $S_{n}$ for the first $n$ terms.

(2) Let $b_{n} = \frac{S_{n}}{n}$. Find the sum $T_{n}$ of the first $n$ terms for the sequence $\{ \frac{1}{b_{n} b_{n+1}} \}$.

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