
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 the sum of the cubes of an infinite number of terms in a geometric progression where $a$ denotes the first term and $-1 < r < 1$ denotes the common ratio. What is the limit of the sum of their cubes?
A) $\frac{a^3}{1 + r^3}$
B) $\frac{a^3}{1 - r^3}$
C) $\frac{3a^3}{1 + r^3}$
D) $\frac{a^3}{1 - r^9}$
E) None of these

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