
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 $$f(x)=2\sin^{2}\left(x+ \frac {3\pi}{2}\right)+ \sqrt {3}\sin(\pi-2x)$$  
(1) If $$x\in[0, \frac {\pi}{2}]$$, find the range of values for $f(x)$;  
(2) Find the interval of increase for the function $$y=\log_{\frac {1}{2}}f(x)$$.

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