
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
Petya made a paper cube and wrote numbers from 1 to 6 on its faces so that the sums of the numbers on any two opposite faces are the same. Vasya wants to cut this cube to get the net shown in the picture. Vasya tries to make the sums of the numbers horizontally and vertically on this net differ as little as possible. What is the smallest positive difference that can be achieved, regardless of how Petya placed the numbers?

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