
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 $f(x)=\sin (ωx+ \frac {π}{6})+ \sin (ωx- \frac {π}{6})-2\cos ^{2} \frac {ωx}{2}, x∈R$ (where $ω > 0$)
(I) Find the range of the function $f(x)$;
(II) If for any $a∈R$, the function $y=f(x)$, $x∈(a,a+π]$ has exactly two distinct intersections with the line $y=-1$, determine the value of $ω$ (proof not required), and find the intervals where the function $y=f(x)$, $x∈R$ is strictly increasing.

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