
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, and $S_n$ is the sum of the first $n$ terms of the sequence $\{a_n\}$, with $a_1=b_1=1$, and $b_3S_3=36$, $b_2S_2=8$.  
(1) Find the general formula for the sequences $\{a_n\}$ 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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