
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
If a quadratic function $f(x)=ax^{2}+bx+c$ has two roots $x_{1}$ and $x_{2}$, then $f(x)=a(x-x_{1})(x-x_{2})$. Similarly, if a cubic function $g(x)=ax^{3}+bx^{2}+cx+d$ has three roots $x_{1}$, $x_{2}$, and $x_{3}$, then $g(x)=$ __________.

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