
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
For which integer values of $p$ and $q$ will the equation $x^{2} + p x + q = 0$ have one root that is 4 times the other? How many solutions do we get if we consider $p$ and $q$ to have at most two digits?



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