
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 $p,$ $q,$ $r,$ $s,$ $t,$ $u$ be nonzero complex numbers such that
\[p = \frac{q + r}{s - 3}, \quad q = \frac{p + r}{t - 3}, \quad r = \frac{p + q}{u - 3},\]
and $st + su + tu = 8$ and $s + t + u = 4,$ find $stu.$

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