
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 geometric progression (GP) with \( n \) terms where the first term is \( a \), and the common ratio is \(-r\). If \( P \) is the product of these \( n \) terms, \( S \) is their sum, and \( S' \) is the sum of their reciprocals, determine \( P \) in terms of \( S, S' \), and \( n \).
A) \( (SS')^{\frac{1}{2}n} \)
B) \( (S/S')^{\frac{1}{2}n} \)
C) \( (S/S')^{\frac{n}{2}} \)
D) \( (SS')^{n-2} \)
E) \( (S/S')^{\frac{1}{2}(n-1)} \)

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