
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
All the numbers 2, 3, 4, 6, 7, 8 are assigned to the six faces of a cube, one number on each face. It is known that the numbers on opposite faces must add up to exactly 11 or 10. For each of the eight vertices of the cube, calculate the product of the three numbers on the faces that include that vertex. What is the greatest possible value of the sum of these eight products?

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