
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
Define $\dfrac{n}{p_{1} + p_{2} + \cdots + p_{n}}$ as the "average reciprocal" of $n$ positive numbers $p_{1}, p_{2}, \ldots, p_{n}$. Given that the sequence $\{a_{n}\}$ has an "average reciprocal" of the first $n$ terms equal to $\dfrac{1}{2n + 1}$, and $b_{n} = \dfrac{a_{n} + 1}{4}$, find the value of $\dfrac{1}{b_{1}b_{2}} + \dfrac{1}{b_{2}b_{3}} + \ldots + \dfrac{1}{b_{2017}b_{2018}}$.

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