
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
Let the arithmetic sequence $\{a_n\}$ have a common difference $d$, and the sum of the first $n$ terms be $S_n$, where $S_n = n^2 + n(a_1 - 1)$ $(n \in N^*,)$ and $a_1, a_3 - 1, a_5 + 7$ form a geometric sequence.

(Ⅰ) Find the general formula for the sequence $\{a_n\}$.

(Ⅱ) Let $b_n = \frac{1}{a_n a_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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