
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 rectangular prism has six faces, twelve edges, and eight vertices. A segment, such as $x$, which joins two vertices not joined by an edge, is called a diagonal. Considering the rectanglular prism has dimensions such that the length, height, and width are all different, calculate how many total diagonals it has and how many of these diagonals are space diagonals?

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