
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 a function $y = A \sin(\omega x + \phi) + m$ with a maximum value of 4, a minimum value of 0, and a smallest positive period of $\frac{2\pi}{\omega}$, and the line $x = \frac{\pi}{\omega}$ is an axis of symmetry for the graph, derive an analytic expression for the function.

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