
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 $f(x)=2 \sqrt {3}\sin \frac {\omega x}{2}\cos \frac {\omega x}{2}+2\cos ^{2} \frac {\omega x}{2}(\omega > 0)$ has a period of $\frac {2\pi}{3}$. When $x\in[0, \frac {\pi}{3}]$, the function $g(x)=f(x)+m$ has exactly two distinct zeros, then the range of the real number $m$ is \_\_\_\_\_.

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