
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 $f(x)=\cos{2\omega x}-\sin{(2\omega x+\frac{\pi}{6})}$ where $\omega>0$, determine the range of values for $\omega$ such that the function has exactly 2 zeros in the interval $\left[0,\pi \right]$.

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