
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 function $f(x)= \sqrt {3}\sin 2x-2\cos ^{2}x$.  
$(1)$ If $\beta\in[0, \frac {\pi}{2}]$, find the range of $f(\beta)$.  
$(2)$ If $\tan \alpha=2 \sqrt {3}$, find the value of $f(\alpha)$.

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