
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 defined on $R$, $f(x)=A\cos (ωx+φ)(A > 0,ω > 0,|φ|≤slant \dfrac {π}{2})$, it is known that: the maximum value is $2$, the distance between two adjacent lowest points on the graph is $π$, and the graph of function $f(x)$ is symmetric about the point $(\dfrac {π}{12},0)$.
(I) Find the analytical expression of $f(x)$;
(II) If vector $ \overrightarrow{a}=(f(x- \dfrac {π}{6}),1)$, $ \overrightarrow{b}=( \dfrac {1}{2},-2\cos x)$, $x∈[- \dfrac {3π}{4}, \dfrac {π}{2}]$, and the function $g(x)= \overrightarrow{a}\cdot \overrightarrow{b}+ \dfrac {1}{2}$, find the range of function $g(x)$.

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