
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
Let a geometric progression with \( n \) terms have first term \( a \neq 1 \), common ratio \( r \), and sum \( s \), where \( r \) and \( s \) are not zero. The sum of the geometric progression formed by replacing each term of the original progression by its reciprocal is?
A) \(\frac{r(1 - r^n)}{a(1 - r)}\)  
B) \(\frac{r(1 - 1/r^n)}{a(r - 1)}\)  
C) \(\frac{(1 - r^n)}{ra(r - 1)}\)  
D) \(\frac{a(r - 1)}{r(1 - 1/r^n)}\)  
E) \(\frac{r(1 - \frac{1}{r^n})}{a(r - 1)}\)

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