
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
The minimum positive period of the function $f(x)=\sin \omega x+ \sqrt {3}\cos \omega x+1$ is $\pi$. When $x\in[m,n]$, $f(x)$ has at least $12$ zeros. The minimum value of $n-m$ is $\boxed{\text{(D) } \frac {16\pi}{3}}$.

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