
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 $f(x)=\sin (\omega x+ \frac {\pi}{6})+\sin (\omega x- \frac {\pi}{6})-2\cos ^{2} \frac {\omega x}{2},x\in\mathbb{R}$ where $\omega > 0$  
$(I)$ Find the range of the function $f(x)$;  
$(II)$ If the graph of the function $y=f(x)$ intersects with the line $y=-1$ at two adjacent points and the distance between these points is $\frac {\pi}{2}$, find the intervals where the function $y=f(x)$ is increasing.

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