
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 parallelepiped (box) with dimensions 2 by 3 by 4 units. Determine the total volume of space inside or within one unit of this box, expressed as \(\frac{m + n\pi}{p}\), where \(m\), \(n\), and \(p\) are positive integers with \(n\) and \(p\) relatively prime. Find \(m+n+p\).

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