
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 $$f(x)= \frac {4\cos^{4}x-2\cos2x-1}{\sin( \frac {\pi}{4}+x)\sin( \frac {\pi}{4}-x)}$$  
(Ⅰ) Find the value of $$f(- \frac {11\pi}{12})$$;  
(Ⅱ) When $$x\in[0, \frac {\pi}{4})$$, find the maximum and minimum values of $$g(x)= \frac {1}{2}f(x)+\sin2x$$.

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