
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 $f(x)=ax^3+bx^2+cx+d$ ($a\neq 0$), define: Let $f''(x)$ be the derivative of the derivative of the function $y=f(x)$, that is, the second 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 $y=f(x)$. Some students found 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." Based on this discovery, for the function $$f(x)=x^3- \frac{3}{2}x^2+3x- \frac{1}{4},$$ its center of symmetry is ___________; calculate $$f\left( \frac{1}{2013}\right)+f\left( \frac{2}{2013}\right)+f\left( \frac{3}{2013}\right)+\cdots +f\left( \frac{2012}{2013}\right)$$ = ___________.

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