
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
Given the line $l$: $y= \sqrt {3}x+4$, a moving circle $O$: $x^{2}+y^{2}=r^{2}(1 < r < 2)$, and a rhombus $ABCD$ with one of its interior angles being $60^{\circ}$. The vertices $A$ and $B$ are on the line $l$, while vertices $C$ and $D$ are on the circle $O$. As $r$ varies, the range of possible values for the area $S$ of rhombus $ABCD$ is \_\_\_\_\_\_.

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