
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 $f(x) = \sin(\omega x + \frac{\pi}{4}) + b$ where $\omega > 0$ has a minimum positive period of $T$, and $\frac{2\pi}{3} < T < \pi$, and the graph of $y = f(x)$ is symmetric about the point $(\frac{3\pi}{2}, 2)$, find $f(\frac{\pi}{2})$.

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