
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
Melissa spilled some ink on her mathematics homework. She cannot determine the coefficient of \(x\), but she notes that the equation whiel spill still maintains two distinct negative integer solutions. The equation looks like:
\[
x^2 + ?x + 48 = 0
\]
What is the sum of all the distinct possible integers that could have been under the ink stain?

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