
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 covering a different quadratic equation. Again, he knows the equation has two distinct negative, integer solutions. This time, he remembers that the product of the roots is 24. What is the sum of all distinct possible integers that could be under the ink stain now?

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