
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 sequence where the first term is $b$ and the common ratio is $q$. Let $n$ be the number of terms. Define $P_c$ as the product of the cubes of these terms, $S_c$ as the sum of the cubes, and $S'_c$ the sum of the reciprocals of these cubes. Express $P_c$ in terms of $S_c$, $S'_c$, and $n$.
**A)** $(S_cS'_c)^{\frac{1}{2}n}$  
**B)** $(S_c/S'_c)^{\frac{1}{2}n}$  
**C)** $(S_cS'_c)^{n-2}$  
**D)** $(S_c/S'_c)^n$  
**E)** $(S_c/S'_c)^{\frac{1}{2}(n-1)}$

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