
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 function $f(x)=ax^{3}+bx^{2}+cx+d$ $(a\neq 0)$ has a center of symmetry at $M(x_{0}, y_{0})$. Let the derivative of $f(x)$ be $f'(x)$, and the derivative of $f'(x)$ be $f''(x)$, then we have $f''(x_{0})=0$. Given the function $f(x)=x^{3}-3x^{2}$, calculate the value of $f(\frac{1}{2013})+f(\frac{2}{2013})+\cdots +f(\frac{4024}{2013})+f(\frac{4025}{2013})$.

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