
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 $f(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0)$, define: $f''(x)$ is the derivative of the derivative of the function $y = f(x)$, $y = f'(x)$. If the equation $f''(x) = 0$ has a real number solution $x_0$, then the point $(x_0, f(x_0))$ is called the "well-behaved point" of the function $y = f(x)$. A student discovered that "every cubic function has a 'well-behaved point'; every cubic function has a symmetry center; and the 'well-behaved point' is the symmetry center." Based on this discovery, answer the question: If the function $g(x) = \frac{1}{3}x^3 - \frac{1}{2}x^2 + 3x - \frac{5}{12}$, then $g(\frac{1}{2017}) + g(\frac{2}{2017}) + g(\frac{3}{2017}) + g(\frac{4}{2017}) + ... + g(\frac{2016}{2017}) = \_\_\_\_\_\_$.

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