
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 $$f(x)=2\cos x\sin\left(x+ \frac {\pi}{6}\right)+\cos^{4}x-\sin^{4}x$$  
(1) Find the smallest positive period of $f(x)$.  
(2) If $$x\in\left[- \frac {\pi}{12}, \frac {\pi}{6}\right]$$, find the maximum and minimum values of $f(x)$ and the corresponding values of $x$.

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