
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 that $\{a_{n}\}$ is an arithmetic sequence, $\{b_{n}\}$ is a geometric sequence, $S_{n}$ is the sum of the first $n$ terms of the sequence $\{a_{n}\}$, $a_{1}=b_{1}=1$, $b_{3}S_{3}=36$, and $b_{2}S_{2}=8 (n \in \mathbb{N}^*)$.

(1) Find $a_{n}$ and $b_{n}$.

(2) If $a_{n} < a_{n+1}$, find the sum of the first $n$ terms, $T_{n}$, of the sequence $\left\{\frac{1}{a_{n}a_{n+1}}\right\}$.

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