
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) with dimensions $4$ by $5$ by $6$ units. This set includes the box, extra space around it, spherical caps at each vertex, and cylindrical wedges along each edge. Calculate the volume of this entire set.

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