
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 $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$), its center of symmetry is $M(x_0, y_0)$. Let the derivative of $f(x)$ be $f'(x)$, and the derivative of $f'(x)$ be $f''(x)$, then we have $f''(x_0) = 0$. If the function $f(x) = x^3 - 3x^2$, calculate the value of $f\left( \frac{1}{2015} \right) + f\left( \frac{2}{2015} \right) + f\left( \frac{3}{2015} \right) + \ldots + f\left( \frac{4028}{2015} \right) + f\left( \frac{4029}{2015} \right)$.

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