
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 $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, with a common difference $d \neq 0$. It's also known that $a_3 + S_5 = 42$, and $a_1$, $a_4$, $a_{13}$ form a geometric sequence.
(Ⅰ) Find the general term formula for the sequence $\{a_n\}$;
(Ⅱ) Let the sequence $b_n = \frac{1}{a_{n-1}a_n}$, find the sum of the first $n$ terms $T_n$ of sequence $\{b_n\}$.

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