
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 that the function $f(x)=\cos x(2 \sqrt {3}\sin x-\cos x)+a\sin ^{2}x$ has a zero point at $\dfrac {π}{12}$.
(1) Find the smallest positive period of the function $f(x)$;
(2) Let $x\in\[- \dfrac {π}{6}, \dfrac {π}{4}\]$, find the maximum and minimum values of $f(x)$ during this time.

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