
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 one unit of a rectangular parallelepiped with dimensions 2 by 3 by 6 units. Calculate the volume of this set given that it includes not only the space inside and exactly one unit around the parallelepiped but also accounts for quarter-cylinders of radius 1 extending from each edge and eighth-spheres of radius 1 at each vertex.

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