
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 again on his homework, but this time on the constant term of his quadratic equation. He can still read the coefficient of $x$, which is 10, but knows that the equation has two distinct negative, integer solutions. What is the sum of all distinct possible integers that could be under the ink stain?

[asy]
draw((0,0)--(3,0)--(3,3)--(0,3)--cycle);
fill((0,0)--(3,0)--(3,3)--(0,3)--cycle,black);
label("$x^2+10x+$",(0,1.5),W);
[/asy]

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