
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 placed at the vertices of a cube, with one number used twice, such that the sum of the numbers on each face of the cube is the same. What is this common sum?

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