
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 $f(x)=6\cos^{2} \frac {ωx}{2}+ \sqrt {3}\sinωx-3$ (ω＞0), the distance between two adjacent symmetry axes on its graph is 4.
(I) Find the value of ω and the interval where the function is monotonically increasing;
(II) If $f(x_{0})= \frac {6 \sqrt {3}}{5}$ and $x_{0}∈( \frac {2}{3}, \frac {14}{3})$, find the value of $f(x_{0}+1)$.

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