
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 $f(x)=4\sin ωx\cdot\cos (ωx+ \frac {π}{6})+1(ω > 0)$, there are two points $A(s,t)$ and $B(s+2π,t)$ on its graph, where $-2 < t < 2$. The line segment $AB$ intersects with the function graph at five points.
(I) Find the value of $ω$;
(II) If the function $f(x)$ is monotonically increasing on $[x\_1,x\_2]$ and $[x\_3,x\_4]$, and monotonically decreasing on $[x\_2,x\_3]$, and satisfies the equation $x\_4-x\_3=x\_2-x\_1= \frac {2}{3}(x\_3-x\_2)$, find all possible values of $x\_1$ and $x\_4$.

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