
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 \( p, \) \( q, \) \( r, \) be distinct complex numbers and \( l, \) \( m, \) \( n \) be distinct non-zero constants such that
\[
\frac{p}{1 - q} = l, \quad \frac{q}{1 - r} = m, \quad \frac{r}{1 - p} = n.
\]
Find the product of all possible values of \( l \times m \times n. \)

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