
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 two units of a rectangular parallelepiped that measures 2 by 3 by 6 units. An additional cylinder with a radius of two units and height of 3 units extends perpendicularly outward from the center of one face of the parallelepiped. Find the volume of this set in the form $\displaystyle \frac{m + n\pi}{p}$, where \textit{m}, \textit{n}, and \textit{p} are integers, and \textit{n} and \textit{p} are relatively prime. Then, find $m+n+p$.

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