
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
The numbers from $1$ to $9$ are arranged on the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. Note: one vertex will not have any number assigned. Calculate the common sum of the numbers on each face of the cube.

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