
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
In the arithmetic sequence $\{a\_n\}$, $a\_1=3$, and the sum of its first $n$ terms is $S\_n$. In the geometric sequence $\{b\_n\}$, all terms are positive, $b\_1=2$, and the common ratio is $q$. It is given that $b\_2+S\_2=16$ and $4S\_2=qb\_2$.

1. Find $a\_n$ and $b\_n$;
2. Let the sequence $\{c\_n\}$ satisfy $c\_n= \frac {1}{S\_n}$, find the sum of the first $n$ terms of $\{c\_n\}$, denoted as $T\_n$.

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