
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
If $T$ is the product of $n$ terms in a geometric sequence, $R$ is the sum of these terms, and $R'$ is the sum of their squares, express $T$ in terms of $R$, $R'$, and $n$.
**A)** $\left(\frac{R'}{R}\right)^n$
**B)** $\left(\frac{R'}{R}\right)^{\frac{n}{2}}$
**C)** $\left(\frac{R'}{R}\right)^{\frac{n-1}{2}}$
**D)** $\left(\frac{R'}{R}\right)^{\frac{n+1}{2}}$
**E)** $\left(\frac{R'}{R}\right)^{n-1}$

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