
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
Eight positive integers are written on the faces of a regular octahedron. Each vertex is labeled with the sum of the three numbers on the faces adjacent to the vertex. If the sum of the numbers on the vertices is equal to 440, what is the sum of the distinct numbers written on the faces?

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