
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
Let \( a_{1}, a_{2}, a_{3}, a_{4} \) be four rational numbers such that the set of their pairwise products 
\[ 
\left\{a_{i} a_{j} \mid 1 \leq i < j \leq 4\right\}=\left\{-24, -2, -\frac{3}{2}, -\frac{1}{8}, 1, 3\right\}. 
\]
Find the value of \( a_{1} + a_{2} + a_{3} + a_{4} \).

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