
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
Given that each vertex of a regular tetrahedron is to be labeled with an integer $1$ through $4$, with each integer being used exactly once, such that the sum of the numbers on the vertices of each triangular face is the same, determine the number of distinct arrangements possible.

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