
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 the arithmetic sequence $\{a_n\}$ has a common difference of $d$, and the solution set of the quadratic inequality $a_{1}x^{2}-dx-3<0$ with respect to $x$ is $(-1, 3)$.

1. Find the general term formula for the sequence $\{a_n\}$.
2. If $b_{n}= \frac {1}{n(a_{n}+3)}$, find the sum of the first $n$ terms, $S_n$, of the sequence $\{b_n\}$.

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