
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