
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
Six positive integers are written on the faces of a cube. Instead of vertices being labeled simply with the product of three adjacent faces, each vertex now has the product divided by 2. The sum of the numbers on these vertices is 1083. Determine the sum of the numbers written on the cube's faces.

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