
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 $f(x)=2\sin ωx\cdot\cos ωx+2A\cos ^{2}ωx-A$ (where $A > 0$, $ω > 0$) with a minimum positive period of $π$ and a maximum value of $2$.

(I) Find the values of $A$ and $ω$;

(II) Given $\frac{π}{6} < θ < \frac{π}{3}$ and $f(θ)= \frac{2}{3}$, find the value of $f(\frac{π}{3} -θ)$.

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