
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 $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$), it is defined that if the equation $f''(x) = 0$ has a real number solution $x_0$, then the point $(x_0, f(x_0))$ is called the "inflection point" of the function $y = f(x)$. A student discovered 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, find the center of symmetry for the function $$f(x) = x^3 - \frac{3}{2}x^2 + 3x - \frac{1}{4}$$.

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