
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 sequence $\{a_n\}$, the average reciprocal of the first $n$ terms is $\dfrac{1}{2n+1}$, and the sequence $\{b_n\}$ is defined as $\dfrac{{a_n}+1}{4}$, calculate $\dfrac{1}{{b_1}{b_2}}+ \dfrac{1}{{b_2}{b_3}}+\cdots+ \dfrac{1}{{b_{2015}}{b_{2016}}}$.

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