
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
Assign the numbers 3, 4, 5, 6, 7, and 8 to the six faces of a cube, one number to each face. For each of the eight vertices of the cube, compute a product of three numbers assigned to the three faces that meet at that vertex. Determine the greatest possible value of the sum of these eight products.

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