
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 that $f''(x)$ is the second derivative of the function $y = f(x)$, and it is defined that if $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$), and the equation $f''(x) = 0$ has a real solution $x_0$, then the point $(x_0, f(x_0))$ is called the center of symmetry of the function $y = f(x)$. It has been observed that "every cubic function has a center of symmetry". Use this discovery to solve the following problem:
Let $g(x) = \frac{1}{3}x^3 - \frac{1}{2}x^2 + 2x + \frac{1}{12}$, find the sum $g\left( \frac{1}{2016} \right) + g\left( \frac{2}{2016} \right) + g\left( \frac{3}{2016} \right) + \ldots + g\left( \frac{2015}{2016} \right)$.

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