
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
A sequence $\{a_n\}$ satisfies $a_1 = 3$ and $S_n = na_n - n(n - 1)$, where $S_n$ is the sum of the first $n$ terms of the sequence.
(Ⅰ) Find the general formula for the $n$-th term, $a_n$.
(Ⅱ) Define $b_n = \frac{1}{a_n \cdot a_{n+1}}$, and 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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