
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 dimensions are in a geometric series. The first dimension is $a$, the second is $ar$, and the third is $ar^2$. The areas of the bottom, side, and front of the box are known. What is the product of these areas equal to?
A) $V^2$
B) $V^3$
C) $a^3r^6$
D) $a^3r^8$
E) $V^9$

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