
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 a cubic function $f(x)=ax^{3}+bx^{2}+cx+d (a \neq 0)$, define $f''(x)$ as the derivative of the derivative $f'(x)$ of the function $y=f(x)$. If the equation $f''(x)=0$ has a real number solution $x_{0}$, then the point $(x_{0},f(x_{0}))$ on $y=f(x)$ is called an "inflection point". Some students discovered that every cubic function has an "inflection point", every cubic function has a symmetry center, and the "inflection point" is the "symmetry center". Based on this discovery, find the symmetry center of the function $f(x)=x^{3}-3x^{2}+3x$.

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