
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 $y = A \sin (\omega x + \varphi) + m$, its maximum value is 4, its minimum value is 0, and its smallest positive period is $\frac{\pi}{2}$. Additionally, the graph is symmetric about the line $x = \frac{\pi}{3}$. If $A > 0$, $\omega > 0$, and $0 < \varphi < \frac{\pi}{2}$, then what is $f(x) = \,\,$ 1.

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