
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
Let the function $f(x)=2\sin (\omega x+\varphi )$, where $x\in \mathbb{R}$, $\omega > 0$, and $|\varphi | < \pi$. If $f\left(\frac{5\pi }{8}\right)=2$, $f\left(\frac{11\pi }{8}\right)=0$, and the smallest positive period of $f(x)$ is greater than $2\pi$, find the values of $\omega$ and $\varphi$.

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