
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
Find the value of the expression $\frac{3\sqrt{12}}{\sqrt{3} + \sqrt{4} + \sqrt{6}}$.
A) $\sqrt{3} + 2\sqrt{2} - \sqrt{6}$
B) $4 - \sqrt{3} - 2\sqrt{2}$
C) $\sqrt{3} - 2\sqrt{2} + \sqrt{6}$
D) $\frac{1}{2}(\sqrt{3} + \sqrt{6} - 2\sqrt{2})$
E) $\frac{1}{3}(2\sqrt{2} + \sqrt{6} - \sqrt{3})$

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