
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
For the cubic function $f(x)=ax^3+bx^2+cx+d$ ($a\ne 0$), we define: Let $f'(x)$ be the derivative of the function $y=f(x)$, and $f''(x)$ be the derivative of the function $f'(x)$. If the equation $f''(x)=0$ has a real 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 through exploration that: every cubic function has an "inflection point"; every cubic function has a center of symmetry, and the "inflection point" is the center of symmetry. Given the function $f(x)=\frac{1}{3}x^3-\frac{1}{2}x^2+3x-\frac{5}{12}$, based on the results of the exploration, find the value of $f(\frac{1}{2018})+f(\frac{2}{2018})+\cdots +f(\frac{2017}{2018})=$______.

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