
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 $f(x)=ax^{3}+bx^{2}+cx+d$ intersects the x-axis at three points $(0,0)$, $(x_{1},0)$, $(x_{2},0)$, and $f(x)$ has extreme values at $x=\frac{3-\sqrt{3}}{3}$, $x=\frac{3+\sqrt{3}}{3}$, calculate the value of $x_{1} \cdot x_{2}$.

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