
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
Consider a cubic function $f(x)=ax^3+bx^2+cx+d (a \neq 0)$. Define a "turning point" as a point $(x_0, f(x_0))$ on the graph of $y=f(x)$ where $x_0$ is a real number solution to the equation ${f''}(x)=0$, where ${f'}(x)$ is the derivative of $f(x)$ and ${f''}(x)$ is the derivative of ${f'}(x)$. A student discovered that every cubic function has a "turning point" and that this point is also the center of symmetry for the function. Given the function $f(x)=\frac{1}{3}x^3-\frac{1}{2}x^2+3x-\frac{5}{12}$, calculate the value of $f\left(\frac{1}{2017}\right) + f\left(\frac{2}{2017}\right) + \cdots + f\left(\frac{2015}{2017}\right) + f\left(\frac{2016}{2017}\right)=\_\_\_\_\_\_\_\_\_\_.$

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