
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
The coefficient of $x$ in Jeremy's math equation is covered in coffee. Jeremy can only see that the equation has two distinct negative integer solutions. The equation displayed on his paper is:

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

What is the sum of all distinct possible integers that could be under the coffee stain?

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