
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 the "harmonic mean" of $n$ positive numbers $a_1, a_2, \cdots, a_n$ as $\dfrac{n}{a_1 + a_2 + \cdots + a_n}$. If it is known that the harmonic mean of the first $n$ terms of the sequence $\{a_n\}$ is $\dfrac{1}{2n+1}$, and $b_n = \dfrac{a_n + 1}{4}$, determine the value of $\dfrac{1}{b_1b_2} + \dfrac{1}{b_2b_3} + \cdots + \dfrac{1}{b_{2017}b_{2018}}$.

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