
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 $f(x)=2\sin (\omega x+\varphi)$ ($\omega > 0$, $0 < \varphi < \pi$) satisfies $f(-x)=f(x)$, and its graph intersects with the line $y=2$ at two points whose x-coordinates are $x_{1}$ and $x_{2}$, respectively, and the minimum value of $|x_{1}-x_{2}|$ is $\pi$, find the values of $\omega$ and $\varphi$.

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