
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 $S_n = 1^2 + 2^2 + 3^2 + \cdots + n^2$, and define
\[ Q_n=\left(\frac{S_2}{S_2-2}\right)^{\frac{1}{2}}\cdot\left(\frac{S_3}{S_3-2}\right)^{\frac{1}{3}}\cdot\cdots\cdot\left(\frac{S_n}{S_n-2}\right)^{\frac{1}{n}} \]
for $n=2,3,4,\cdots$. Compute $Q_6$.
A) 1.01
B) 1.03
C) 1.048
D) 1.10

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