
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 the function y=f(x) have the domain D. If for any x1, x2 ∈ D, when x1+x2=2a, it always holds that f(x1)+f(x2)=2b, then the point (a,b) is called the symmetry center of the graph of the function y=f(x). Investigate a symmetry center of the function f(x)=x+sinπx-3, and find the value of f(1/2016)+f(2/2016)+f(3/2016)+...+f(4030/2016)+f(4031/2016).

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