
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
Study the function $f(x)=x+\sin \pi x-3$. Given that a symmetry center of the function is $(a,b)$, determine the value of $f\left( \dfrac{1}{2017}\right)+f\left( \dfrac{2}{2017}\right)+f\left( \dfrac{3}{2017}\right)+...+f\left( \dfrac{4032}{2017}\right)+f\left( \dfrac{4033}{2017}\right)$.

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