
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
In the vertices of a cube, the numbers \(1^{2}, 2^{2}, \ldots, 8^{2}\) are placed (each number in one vertex). For each edge, the product of the numbers at its ends is calculated. Find the maximum possible sum of all these products.

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