
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 $f(x)=2\sin (\omega x+\varphi)-1$ ($\omega > 0$, $|\varphi| < \pi$) has a zero at $x= \frac {\pi}{3}$, and one of the symmetry axes of the graph of $y=f(x)$ is $x=- \frac {\pi}{6}$, find the monotonic interval of the function $f(x)$ when $\omega$ takes its minimum value.

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