
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 vertices at the corners and edges joining them similarly to a cube. The prism dimensions differ along each axis; therefore, no two adjoining sides are of the same length. If one side has a length ratio of 2:3 with another, and there are three dimensions under consideration, compute how many total diagonals (both face diagonals that lie within the surfaces and space diagonals that span the entire prism) exist.

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