
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 $f(x) = 2\cos x \sin \left(x + \dfrac{\pi}{6}\right) + \cos^4 x - \sin^4 x$,  
$(1)$ find the smallest positive period of $f(x)$;  
$(2)$ if $x \in \left[- \dfrac{\pi}{12}, \dfrac{\pi}{6}\right]$, 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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