
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
In the vertices of a cube, numbers from 1 to 8 are written, and on each edge, the absolute value of the difference of the numbers at its ends is written. What is the minimum number of different numbers that can be written on the edges?

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