
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 quadratic equation on Sofia’s homework is partially erased. She knows that the equation has two distinct negative integer solutions. Find the sum of all the distinct possible integers that could replace the missing coefficient of $x$ in Sofia’s equation, given that the constant term when the quadratic equation $(x^2 + bx + c = 0)$ is written is $24$.

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