
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, let $S_{n}$ denote the sum of its first $n$ terms, where $n \in \mathbb{N}^*$. If $S_{3} = a_{4} + 2$ and $a_{1}$, $a_{3}$, $a_{13}$ form a geometric sequence:

(1) Find the general term formula for $\{a_{n}\}$;
(2) Let $b_{n} = \frac{1}{a_{n}a_{n+1}}$, find the sum $T_{n}$ of the first $n$ terms of the sequence $\{b_{n}\}$.

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