
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 the variables satisfying the relationships \(xy = a\), \(xz = b\), and \(yz = c\), and none of these quantities is zero, the expression \(x^3 + y^3 + z^3\) can be expressed in terms of \(a\), \(b\), and \(c\) as:
A) \(\frac{a^2+b^2+c^2}{abc}\)
B) \(\frac{a^3+b^3+c^3}{abc}\)
C) \(abc(a^3+b^3+c^3)\)
D) \(\frac{(a+b+c)^3}{abc}\)

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