
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 $f(x)=\cos x\bullet \sin (x+\frac{\pi }{3})-\sqrt{3}\cos^{2}x+\frac{\sqrt{3}}{4}$, where $x\in R$.

(1) Find the minimum positive period and symmetry center of $f(x)$.

(2) If the graph of the function $y=g(x)$ is obtained by shifting the graph of $y=f(x)$ to the left by $\frac{\pi }{4}$ units, find the maximum and minimum values of $g(x)$ on the interval $\left[-\frac{\pi }{6},\frac{\pi }{3}\right]$.

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