
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 $p, q, r, u, v, w$ be nonzero complex numbers such that
\[p = \frac{q + r}{u - 3}, \quad q = \frac{p + r}{v - 3}, \quad r = \frac{p + q}{w - 3},\]
and $uv + uw + vw = 7$ and $u + v + w = 4$, find $uvw$.

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