
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 $S_{n}$ is the sum of the first $n$ terms of the arithmetic sequence $\{a_{n}\}$, $a_{1}=1$, and $a_{8}=3a_{3}$, then $\dfrac{a_{2}}{S_{1}S_{2}}+ \dfrac{a_{3}}{S_{2}S_{3}}+ \dfrac{a_{4}}{S_{3}S_{4}}+\ldots+ \dfrac{a_{n+1}}{S_{n}S_{n+1}}=$ \_\_\_\_\_\_.

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