
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
Let \(a\), \(b\), \(c\), \(x\), \(y\), \(z\) be nonzero complex numbers such that
\[a = \frac{b + c}{x - 3}, \quad b = \frac{a + c}{y - 3}, \quad c = \frac{a + b}{z - 3},\]and \(xy + xz + yz = 10\) and \(x + y + z = 6\), find \(xyz\).

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