
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
Consider a rectangular prism with lengths of edges 4 units, 6 units, and 8 units. Calculate the total number of diagonals within this prism, where a diagonal is either a segment joining two vertices on the same face not directly connected by an edge (face diagonal), or a segment joining two vertices that are not on the same face (space diagonal).

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