
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
Suppose each vertex of a tetrahedron needs to be labeled with an integer from $1$ to $4$, each integer being used exactly once, so that the sum of the numbers on the vertices of each face is the same for all four faces. Arrangements that can be rotated into each other are considered identical. Determine the number of different such arrangements that are possible.

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