
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 $\{a\_n\}$, $a\_1=b\_1=1$, and $b\_3S\_3=36$, $b\_2S\_2=8$.

1. Find the general term formula for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. If $a\_n < a\_{n+1}$, find the sum $T\_n$ of the first $n$ terms of the sequence $\{ \frac {1}{a\_n a\_{n+1}} \}$.

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