
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]


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For the cubic function $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$), we define: $f''(x)$ is the derivative of the derivative of the function $y = f(x)$, denoted as $f'(x)$. 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, the center of symmetry for the function $f(x) = x^3 - 3x^2 + 3x$ is __________.

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