
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
Numbers \(1^2, 2^2, \ldots, 8^2\) are placed at the vertices of a cube (one number at each vertex). For each edge of the cube, the product of the numbers at its endpoints is calculated. Find the largest possible sum of all these products.

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