
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
Let $f(x)=\sin (\omega x+\frac{π}{4})+b$ where $\omega \gt 0$. The smallest positive period of the function is $T$. If $\frac{2π}{3} \lt T \lt \pi $, and the graph of $y=f(x)$ is symmetric about the point $(\frac{3π}{2},2)$, find the value of $f(\frac{π}{2})$.

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