
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
Let $y = f(x)$ be a function with domain D. If for any $x_1, x_2 \in D$ satisfying $x_1 + x_2 \neq 2a$, it always holds that $f(x_1) + f(x_2) = 2b$, then the point $(a, b)$ is called the center of symmetry for the graph of the function $y = f(x)$. Study and use the center of symmetry for the function $f(x) = x^3 - 3x^2 - \sin(\pi x)$ to calculate the value of 
$$
S = f\left( \frac {1}{2015} \right) + f\left( \frac {2}{2015} \right) + \ldots + f\left( \frac {4028}{2015} \right) + f\left( \frac {4029}{2015} \right).
$$

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