
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
Given a geometric progression with first term $a$ and common ratio $r$ where $-1 < r < 1$, calculate the limit of the sum of the cubes of the terms in the series.
**A)** $\frac{a^3}{1 + r^3}$  
**B)** $\frac{a^3}{1 - r^3}$  
**C)** $\frac{a^3}{1 - r^2}$  
**D)** $\frac{a^3}{1 + r}$  
**E)** $\text{none of these}$

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