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

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