
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
Pablo is solving a quadratic equation and notices that the ink has smeared over the coefficient of $x$, making it unreadable. He recalls that the equation has two distinct negative, integer solutions. He needs to calculate the sum of all possible coefficients that were under the smeared ink. 

Given the equation form: 
\[ x^2 + ?x + 24 = 0 \]

What is the sum of all distinct coefficients that could complete this equation?

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