
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) that measures 2 by 3 by 6 units. Given that the volume of this set is $\displaystyle {{m+n\pi}\over p}$, where $m$, $n$, and $p$ are positive integers, and $n$ and $p$ are relatively prime, find $m+n+p$.

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