
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:
\[
\left\{a_i a_j \mid 1 \leq i < j \leq 4\right\} = \left\{-24, -2, -\frac{3}{2}, -\frac{1}{8}, 1, 3\right\}
\]
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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