
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 any cubic function $f(x)=ax^2+bx^2+cx+d (a\neq 0)$, it has a symmetry center $M(x_0, f(x_0))$. Let the derivative of the function $f(x)$ be $f′(x)$, and the derivative of $f′(x)$ be $f″(x)$. Then, $f″(x_0)=0$. If the function $f(x) = x^3 - 3x^2$, then find the value of $f(\frac{1}{2016}) + f(\frac{2}{2016}) + f(\frac{3}{2016}) + ... + f(\frac{4031}{2016}) = \_\_\_\_\_\_$.

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