
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 the function $f(x)= \dfrac {(\sin x+\cos x)^{2}-1}{\cos ^{2}x-\sin ^{2}x}$, the equation $f(x)= \sqrt {3}$ has solutions in the interval $(0,+\infty)$, which are arranged in ascending order to form the sequence $\{a_{n}\}(n\in\mathbb{N}^{*})$.  
$(1)$ Find the general formula for the sequence $\{a_{n}\}$.  
$(2)$ Let $b_{n}= \dfrac {3a_{n}}{(4n^{2}-1)(3n-2)}$, and the sum of the first $n$ terms of the sequence $\{b_{n}\}$ be $S_{n}$. Find the expression for $S_{n}$.

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