
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 $f(x)=2\sin(\omega x+\varphi)$, where $(\omega > 0, 0 < \varphi < \pi)$, has a minimum positive period of $\pi$ and passes through the point $({\frac{π}{4},\sqrt{2}})$. <br/>$(1)$ Find the analytical expression of the function $f(x)$; <br/>$(2)$ Determine the intervals where the function $f(x)$ is monotonically increasing.

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