
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 $xy + xz + yz = 7$ and $x + y + z = 4,$ find $xyz.$

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