
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 \(p\) and \(q\) be constants. Suppose the equation:
\[\frac{(x+p)(x+q)(x-8)}{(x+4)^2} = 0\]
has exactly 3 distinct roots, while the equation:
\[\frac{(x+4p)(x-4)(x-10)}{(x+q)(x-8)} = 0\]
has exactly 2 distinct roots. Compute \(50p - 10q.\)

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