
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 \( S_n = 2 + 4 + 6 + \cdots + 2n \) be the sum of the first n even numbers and let
\[ Q_n = \frac{S_2}{S_2 - 2} \cdot \frac{S_3}{S_3 - 2} \cdot \frac{S_4}{S_4 - 2} \cdot \cdots \cdot \frac{S_n}{S_n - 2} \]
for \( n = 2, 3, 4, \ldots \), calculate \( Q_{20} \).
A) \(11.5\)
B) \(11.67\)
C) \(12.0\)
D) \(35\)

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