
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 that the graph of the function $y=f(x)$ is symmetric about the line $x=\frac{π}{3}$ (Condition 1), or symmetric about the point $P(\frac{π}{6},0)$ (Condition 2), or passes through the point $Q(\frac{2π}{3},-2)$ (Condition 3), choose one of these conditions and complete the following questions:

Question: Given the function $f(x)=2\sin ωx\cosφ+2\cos ωx\sinφ$ ($ω>0$, $|φ|<\frac{π}{2}$) with the smallest positive period of $\pi$.
$(Ⅰ)$ Find the analytical expression of the function $f(x)$.
$(Ⅱ)$ Determine the maximum and minimum values of the function $f(x)$ on the interval $[\frac{π}{6},\frac{π}{2}]$.

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