
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
Milton spilled ink on another part of his homework where another quadratic equation was written. He remembers that this equation also has two distinct negative integer roots but the product of the roots has changed. He knows the product of the roots is 48. What is the sum of all distinct possible integers that could be under the ink stain for this new equation?

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