
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
$R$ is directly proportional to $S$ and inversely proportional to $T$. Given that $R = 2$, $S = 1$, and $T = 4$, find $S$ when $R = 3\sqrt{3}$ and $T = 4 \sqrt{2}$.
**A)** \( \frac{3}{2} \)
**B)** \( \frac{3\sqrt{3}}{2} \)
**C)** \( 6 \)
**D)** \( \frac{3\sqrt{6}}{2} \)
**E)** \( 4\sqrt{2} \)

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