
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 \( f(x) = \sin (\omega x + \varphi) \) with \( \omega > 0 \) and \( 0 \leq \varphi \leq \pi \), which is an even function on \(\mathbf{R}\). Its graph is symmetric with respect to the point \( M\left(\frac{3}{4} \pi, 0\right) \) and is monotonous on the interval \(\left[0, \frac{\pi}{2}\right]\). Find the values of \(\omega\) and \(\varphi\).

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