
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
If the function $f(x)=\sin \omega x+\sqrt{3}\cos \omega x$ $(x\in \mathbb{R})$, and $f(\alpha)=-2,f(\beta)=0$, with the minimum value of $|\alpha -\beta|$ being $\frac{3\pi}{4}$, determine the value of the positive number $\omega$.

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