
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 has eight vertices and twelve edges. If a diagonal is a segment joining any two vertices not on the same edge, how many total diagonals are there in the cube, distinguishing between face diagonals (diagonals on the same face) and space diagonals (diagonals connecting vertices not on the same face)?

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