
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
Numbers $1,2,3,4,5,6,7,$ and $8$ are placed at the vertices of a cube such that the sum of any three numbers belonging to any face of the cube is not less than 10. Find the minimum possible sum of four numbers belonging to one face.

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