
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 set of points that are inside or within two units of a rectangular parallelepiped (box) that measures $5$ by $6$ by $7$ units. Calculate the volume of this set, expressed as $\frac{m + n\pi}{p},$ where $m, n,$ and $p$ are positive integers, with $n$ and $p$ relatively prime.

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