
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
Let $x=1$ be an extremum point of the function $f(x)=a_{n+1}x^{3}-a_{n}x^{2}-a_{n+2}x+1$ $(n\in N_{+})$, and the sequence $\{a_{n}\}$ satisfies $a_{1}=1$, $a_{2}=2$, $b_{n}=\log_{2}a_{n+1}$. Find the value of $\left[\dfrac{2018}{b_{1}b_{2}} +\dfrac{2018}{b_{2}b_{3}} +...+\dfrac{2018}{b_{2018}b_{2019}} \right]$.

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