
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
(48th Slovenian Mathematical Olympiad Problem) We write a positive integer on each face of a cube. Then, at each vertex, we write a number that equals the product of the integers on the three faces meeting at that vertex. Given that the sum of the numbers at all the vertices is 70, find the sum of the numbers on all the faces of the cube.

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