
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 $f(x) = A\sin(x + \varphi)$ ($A > 0$, $0 < \varphi < \pi$) has a maximum value of 1, and its graph passes through point M ($\frac{\pi}{3}$, $\frac{1}{2}$), then $f(\frac{3\pi}{4})$ = \_\_\_\_\_\_.

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