
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 $f(x)=\cos(\omega x+\frac{π}{3})$, if $m$ and $n$ are two distinct roots of the equation $f(x)=\frac{1}{2}$ and satisfy the condition that the minimum value of $|m-n|$ is $\frac{π}{6}$, find the value of $\omega$.

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