
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 $f(x) = \sin(\omega x + \varphi)$ where $(0 < \omega < 1, 0 \leq \varphi \leq \pi)$ is an even function on $R$, and its graph is symmetric about the point $M(\frac{3\pi}{4}, 0)$.
$(1)$ Find the values of $\varphi$ and $\omega$;
$(2)$ For $x \in [-\frac{3\pi}{4}, \frac{\pi}{2}]$, find the maximum and minimum values of $f(x)$.

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