
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 given the cubic equation:

\[ x^{3}-(a+b+c) x^{2}+(a b+a c+b c) x = a b c \]

then \( a, b \), and \( c \) are the roots of this equation.

Verify with the equations:

\[ 
\begin{aligned}
& \text{1) } x^{3}-6 x^{2}+11 x-6=0 \\
& \text{2) } x^{3}-4 x^{2}-4 x+16=0 
\end{aligned}
\]

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