
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 $C$ be a right rectangular prism with edge lengths $2,$ $4,$ and $5$, along with its interior. Denote the set of points in $3$-dimensional space that lie within a distance $r\geq0$ from any point in $C$ as $T(r)$. The volume of $T(r)$ can be expressed in the form $ar^3 + br^2 + cr + d$, where $a,$ $b,$ $c,$ and $d$ are positive constants. Determine the value of $\frac{bc}{ad}$.
A) 14.5
B) 15.675
C) 16 
D) 17
E) 18

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