
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
Let \( S \) be a subset with four elements chosen from \(\{1, 2, \ldots, 10\}\). Michael notes that there is a way to label the vertices of a square with elements from \( S \) such that no two vertices have the same label, and the labels adjacent to any side of the square differ by at least 4. How many possibilities are there for the subset \( S \)?

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