
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]


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Given an arithmetic sequence $\{a\_n\}(n∈N^*)$, let $S\_n$ denote the sum of its first $n$ terms. Also, given $a\_3=5$, $S\_3=9$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $\{b\_n\}(n∈N^*)$ be a geometric sequence with the sum of its first $n$ terms denoted by $T\_n$. If $q > 0$, $b\_3=a\_5$, and $T\_3=13$, find $T\_n$.
3. If $b\_n= \frac {1}{a\_n a\_{n+1}}$, find the sum of the first $n$ terms for the sequence $\{b\_n\}$, $S\_n$.

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