
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 $f(x)=\sin \omega x \cos \omega x - \sqrt{3} \cos^2 \omega x$, where $(\omega > 0)$, ${x}_{1}$ and ${x}_{2}$ are the two zeros of the function $y=f(x)+\frac{2+\sqrt{3}}{2}$, and $|x_{1}-x_{2}|_{\min }=\pi$. When $x\in[0,\frac{7\pi}{12}]$, the sum of the minimum and maximum values of $f(x)$ is ______.

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