
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 $f(x)=4\cos x\sin (x+ \frac{π}{6})$,

(1) Find the smallest positive period of $f(x)$;

(2) Find the symmetry axis and symmetry center of the graph of $f(x)$;

(3) Find the solution set for $f(x)\leqslant 0$;

(4) Find the maximum and minimum values of $f(x)$ in the interval $[- \frac{π}{6}, \frac{π}{4}]$.

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