
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 that the graph of the function $f(x) = ax^3 + bx^2 + cx + d$ has three distinct intersection points with the x-axis at $(0, 0)$, $(x_1, 0)$, and $(x_2, 0)$, and $f(x)$ has extreme values at $x=1$ and $x=2$, then the value of $x_1 \cdot x_2$ is ______.

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