
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 that $\sin \varphi = \frac{3}{5}$ and $\varphi \in (\frac{\pi}{2}, \pi)$, the distance between two adjacent symmetry axes of the graph of the function $f(x) = \sin(\omega x + \varphi) (\omega > 0)$ is equal to $\frac{\pi}{2}$. Find the value of $f(\frac{\pi}{4})$.

A) $-\frac{3}{5}$
B) $-\frac{4}{5}$
C) $\frac{3}{5}$
D) $\frac{4}{5}$

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