
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 $f(x) = x + \sin(\pi x) - 3$, study its symmetry center $(a, b)$ and find the value of $f\left( \frac {1}{2016} \right) + f\left( \frac {2}{2016} \right) + f\left( \frac {3}{2016} \right) + \ldots + f\left( \frac {4030}{2016} \right) + f\left( \frac {4031}{2016} \right)$.

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