
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 3, 4, 5, 6, 7, 8 are assigned to the six faces of a cube, one number to each face. There is an additional condition that 3 and 4, which are the smallest numbers, must be on opposite faces. For each of the eight vertices of the cube, a product of three numbers is computed, where the three numbers are the numbers assigned to the three faces that meet at that vertex. What is the greatest possible value of the sum of these eight products?

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