
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 \(a\) a positive real number, let \(x_{1}, x_{2}, x_{3}\) be the roots of the equation \(x^{3}-a x^{2}+a x-a=0\). Determine the smallest possible value of \(x_{1}^{3}+x_{2}^{3}+x_{3}^{3}-3 x_{1} x_{2} x_{3}\).

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