
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
Place the numbers 1, 2, 3, 4, 2, 6, 7, and 8 at the eight vertices of a cube such that the sum of the numbers on any given face is at least 10. Determine the minimum possible sum of the numbers on each face.

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