
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 definition of a cubic function $f(x)=ax^3+bx^2+cx+d (a\neq 0)$, where $f'(x)$ is the derivative of $f(x)$ and $f''(x)$ is the derivative of $f'(x)$. 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" and a symmetry center, and the inflection point is the symmetry center. If $f(x)=\frac{1}{3}x^3-\frac{1}{2}x^2+3x-\frac{5}{12}$, please find:

(1) The symmetry center of the function $f(x)=\frac{1}{3}x^3-\frac{1}{2}x^2+3x-\frac{5}{12}$ is \_\_\_\_\_\_\_\_\_\_;

(2) The value of $f(\frac{1}{2014})+f(\frac{2}{2014})+\ldots +f(\frac{2013}{2014})=$\_\_\_\_\_\_\_\_\_\_.

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