
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 again, obscuring the coefficient of $x$, but he remembers that the equation still has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain now?

[asy]
draw((0,0)--(3,0)--(3,3)--(0,3)--cycle);
fill((0,0)--(3,0)--(3,3)--(0,3)--cycle,black);
label("$x+48=0$",(3,1.5),E);
label("$x^{2}+$",(0,1.5),W);
[/asy]

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