
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
Each vertex of a regular tetrahedron is to be labeled with a unique integer from $1$ through $4$, and the sum of the numbers on the vertices of each face is the same for all four faces. How many different arrangements are possible?

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