
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 ${ω>0,-\frac{π}{2}<φ<\frac{π}{2}}$ has a minimum positive period of $\pi$, and $f(\frac{π}{4})=1$. <br/>$(1)$ Find $\omega$ and $\varphi$;<br/>$(2)$ Let $g(x)$ be the function obtained by shifting the graph of $f(x)$ to the right by $\frac{π}{3}$ units. Find the maximum value of $f(x)+g(x)$ and the set of $x$ values at that time.

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