
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 $l: y= \sqrt {3}x+4$, and a moving circle $O: x^{2}+y^{2}=r^{2}$ ($1<r<2$), a rhombus $ABCD$ has an internal angle of $60^\circ$, with vertices $A$, $B$ on line $l$, and vertices $C$, $D$ on circle $O$. As $r$ changes, the range of the area $S$ of rhombus $ABCD$ is \_\_\_\_\_\_.

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