
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 the set of points that are inside or within one unit of a rectangular parallelepiped (box) measuring $4 \times 5 \times 6$ units. Calculate the volume of this set, given in the form $\frac{m + n\pi}{p}$, where $m, n,$ and $p$ are positive integers, and $n$ and $p$ are relatively prime. Then find $m + n + p.$

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