
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
Petya tells Kolya: "I placed some numbers at the vertices of a cube, and then wrote the sum of the four numbers at its vertices on each face. Then, I added all six numbers on the faces and got 2019. Can you find out the sum of the eight numbers at the vertices of the cube?" How would you answer this question if you were Kolya?

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