
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
Let  $B$  be a  $1 \times 2 \times 4$  box (rectangular parallelepiped).  Let  $R$  be the set of points that are within distance 3 of some point in  $B$ .  (Note that  $R$  contains  $B$ .)  What is the volume of  $R$ ?

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