
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 cubic function $f(x)=ax^{3}+bx^{2}+cx+d (a\neq 0)$, the definition of an inflection point is provided: If the equation $f′′(x)=0$ has a real number solution $x_{0}$, then the point $(x_{0},f(x_{0}))$ is called the "inflection point" of the function $y=f(x)$. A student discovered that every cubic function has an inflection point, which is also the function's center of symmetry. If $f(x)=\frac{1}{3} x^{3}-\frac{1}{2} x^{2}+3x-\frac{5}{12}$,

(1) Find the function's center of symmetry.

(2) Calculate $f(\frac{1}{2019}) +f(\frac{2}{2019}) +f(\frac{3}{2019}) +f(\frac{4}{2019}) +...+f(\frac{2018}{2019})$.

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