
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
A cube is circumscribed around a sphere of radius 1. From one of the centers of the cube's faces, vectors are drawn to all other face centers and vertices. The dot products of each pair of these vectors are calculated, totaling 78. What is the sum of these dot products?

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