
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 a cubic function $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$), the definition of an inflection point is provided: Let $f'(x)$ be the derivative of $y = f(x)$, and let $f''(x)$ be 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 an "inflection point" of the function $y = f(x)$. A student discovered that every cubic function has an "inflection point" and a center of symmetry, and that the "inflection point" is the center of symmetry. Let the function be $$g(x) = \frac{1}{3}x^3 - \frac{1}{2}x^2 + 3x - \frac{5}{12}$$. Find the value of $$g(\frac{1}{2018}) + g(\frac{2}{2018}) + \ldots + g(\frac{2017}{2018})$$.

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