
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 definition: Let ${f'}\left(x\right)$ be the derivative of the function $y=f\left(x\right)$, and $f''\left(x\right)$ be the derivative of the function ${f'}\left(x\right)$. If the equation $f''\left(x\right)=0$ has a real number solution $x=x_{0}$, then $((x_{0}$,$f(x_{0}))$ is called the "inflection point" of the function $y=f\left(x\right)$. After studying, it was found that all cubic functions, $f\left(x\right)=ax^{3}+bx^{2}+cx+d\left(a\neq 0\right)$, have "inflection points", and this "inflection point" is also the symmetric center of the graph of the function $y=f\left(x\right)$. Given the function $f(x)=\frac{1}{3}{x}^{3}-\frac{1}{2}{x}^{2}+3x-\frac{5}{12}$.  
$(1)$ Find the symmetric center of $f\left(x\right)$;  
$(2)$ Find the value of $f(\frac{1}{2023})+f(\frac{2}{2023})+…+f(\frac{2022}{2023})$.

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