
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
In the vertices of a cube, the numbers ±1 are placed, and on its faces, the numbers are equal to the product of the numbers at the vertices of that face. Find all possible values that the sum of these 14 numbers can take. Indicate their product in the answer.

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