
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 some ink on his homework paper again. This time, he can't read the coefficient of $x$, but he remembers that the quadratic equation has two distinct negative, integer solutions. What is the sum of all possible distinct integers that could be under the ink stain if the constant term he can faintly make out is 24?

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