
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
A cube-shaped storage box has dimensions proportional to $3x$, $4x$, and $5x$. Given that the bottom area is $12x^2$, a side area is $15x^2$, and the front area is $20x^2$, what is the product of these three areas equal to?
**A)** $120x^3$    
**B)** $3600x^6$  
**C)** $1200x^6$  
**D)** $600x^6$    
**E)** $36000x^6$

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