
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 a function $f(x) = ax^3 + bx^2 + cx + d \ (a \neq 0)$, its center of symmetry is $M(x_0,y_0)$. Let the first derivative of the function $f(x)$ be $f'(x)$, and the second derivative of $f(x)$ be $f''(x)$. Then we have $f''(x) = 0$. If the function is given by $f(x) = x^3 - 3x^2$, find the value of $f\left(\frac{1}{2013}\right) + f\left(\frac{2}{2013}\right) + \cdots + f\left(\frac{4024}{2013}\right) + f\left(\frac{4025}{2013}\right)$.

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