
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
For the cubic function $f(x)=ax^{3}+bx^{2}+cx+d$ ($a\neq 0$), let's define it; let $f′(x)$ be the derivative of the function $y=f(x)$, and $f″(x)$ be the derivative of the function $f′(x)$. If the equation $f″(x)=0$ has a real solution $x_{0}$, then the point $(x_{0},f(x_{0}))$ is called the "inflection point" of the function $y=f(x)$. A student found through exploration that any cubic function has an "inflection point"; every cubic function has a center of symmetry, and the "inflection point" is the center of symmetry. Given the function $f(x)=\dfrac{1}{3}{{x}^{3}}-\dfrac{1}{2}{{x}^{2}}+3x-\dfrac{5}{12}$.

Based on the results of the exploration, calculate $f(\dfrac{1}{2017})+f(\dfrac{2}{2017})+f(\dfrac{3}{2017})+...+f(\dfrac{2016}{2017})=\boxed{\text{answer}}$．

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