
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 rectangular box where the areas of the bottom, front, and one side are expressed in terms of length $x$, width $y$, and height $z$ respectively as $3xy$, $2yz$, and $3xz$. Determine the correct relation between the product of these areas and a transformed property of the volume of the box.

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