
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 $f(x)=Asin(ωx+φ)$ where $(A>0, ω>0, |φ|<\frac{π}{2})$ has a minimum positive period of $\pi$, and the point $P(\frac{π}{6},2)$ is the highest point on the graph of this function.  
$(1)$ Find the analytical expression of the function $f(x)$.  
$(2)$ Shift the graph of the function $f(x)$ to the right by $\theta (0<θ<\frac{π}{2})$ units to obtain the graph of the function $g(x)$. The function $g(x)$ is increasing on $[0,\frac{π}{4}]$. Find the range of values for $\theta$.

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