
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
The sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n= \frac {n^2}{an+b}$. Given $a_1= \frac {1}{2}$, $a_2= \frac {5}{6}$,  
$(1)$ Find the sum of the first $n$ terms $S_n$ and the general formula for the sequence $\{a_n\}$;  
$(2)$ Let $b_n= \frac {a_n}{n^2+n-1}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$. Determine the smallest positive integer $n$ such that $T_n > \frac {2006}{2016}$.

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