
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 "harmonic mean" of n positive numbers $a_{1}$, $a_{2}$, …$a_{n}$ is defined as $\frac{n}{a_{1}+a_{2}+…+a_{n}}$, if the harmonic mean of the first n terms of the sequence ${a_{n}}$ is $\frac{1}{2n+1}$, and $b_{n}= \frac{a_{n}+1}{4}$, calculate the value of $\frac{1}{b_{1}b_{2}}+ \frac{1}{b_{2}b_{3}}+…+ \frac{1}{b_{2016}b_{2017}}$.

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