
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 $f(x)=\sin (ωx+φ)$, where $(ω > 0,|φ|≤slant \dfrac {π}{2})$, one of its highest points is $(\dfrac {8}{3},1)$, and a neighboring zero point is $\dfrac {14}{3}$.
(I) Find the analytical expression of $f(x)$;
(II) Find the range of values of $g(x)=f(x)-2\cos ^{2} \dfrac {π}{8}x+1$, where $x∈[\dfrac {2}{3},2]$.

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