
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 values for $f(\beta)$;
(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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