
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
A damaged portion of a mathematical worksheet hides the coefficient of $x$ in a quadratic equation. The equation is known to have two distinct positive, integer solutions. Determine the sum of all possible integers that could be obscured by the damage.

[asy]
draw((0,0)--(3,0)--(3,3)--(0,3)--cycle);
fill((0,0)--(3,0)--(3,3)--(0,3)--cycle,black);
label("$x^2+$",(1.5,1.5),W);
label("$=24$",(3,1.5),E);
[/asy]

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