
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 $f(x)=2\sin (\omega x+ \frac {\pi}{6})-4\cos ^{2} \frac {\omega x}{2}+3$ where $\omega > 0$ and $x\in\mathbb{R}$.  
(I) Find the range of the function $f(x)$.  
(II) If the distance between two adjacent intersections of the graph of the function $f(x)$ and the line $y=1$ is $\frac {\pi}{2}$, find the intervals where the function $f(x)$ is monotonically decreasing.

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