
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 $f(x)=ax^{3}+bx^{2}+cx+d (a\neq 0)$, the definition of an "inflection point" is provided: Let $f′(x)$ be the derivative of the function $y=f(x)$, and $f″$ 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 this inflection point is also the center of symmetry for the function. Based on this discovery, find the center of symmetry for the function $f(x)= \frac{1}{3}x^{3}- \frac{1}{2}x^{2}+3x- \frac{5}{12}$.

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