
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 geometric series with first term $a$ and common ratio $r$ (where $-1 < r < 1$) is considered. Determine the limit of the sum of the cubes of the terms in this geometric progression.
**A)** $\frac {a^3}{1 + r^3}$  
**B)** $\frac {a^3}{1 - r^3}$  
**C)** $\frac {a^3}{1 + r^6}$  
**D)** $\frac {3a^3}{1 - r^3}$

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