
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 $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$), we define: Let $f'(x)$ be the derivative of the function $y = f(x)$, and $f''(x)$ be the derivative of $f'(x)$. 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. If $$f(x) = \frac{1}{3}x^3 - \frac{1}{2}x^2 + 2x + \frac{1}{12}$$, based on this discovery,
(1) Find the center of symmetry of the cubic function $$f(x) = \frac{1}{3}x^3 - \frac{1}{2}x^2 + 2x + \frac{1}{12}$$;
(2) Calculate $$f\left(\frac{1}{2017}\right) + f\left(\frac{2}{2017}\right) + f\left(\frac{3}{2017}\right) + \ldots + f\left(\frac{2016}{2017}\right)$$.

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