
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 is given by $f(x) = \sin \omega x - \sqrt{3} \cos \omega x$ with $\omega > 0$ and $x \in \mathbb{R}$, and it's known that $f(x_1) = 2$, $f(x_2) = 0$, and the minimum value of $|x_1 - x_2|$ is $\frac{3\pi}{2}$, calculate the value of $\omega$.

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