
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
A regular hexagon with an area of $\frac {3 \sqrt {3}}{2}$ has all its vertices on the surface of sphere O. The distance from the center O of the sphere to the plane containing the hexagon is $2 \sqrt {2}$. Let the volume of sphere O be $V$ and the surface area of sphere O be $S$, calculate the value of $\frac {V}{S}$.

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