
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 $f(x) = \sin(\omega x + \varphi)$ ($\omega > 0$, $-\frac{π}{2} < \varphi < \frac{π}{2}$) have a minimum positive period of $T$, and $f(T) = \frac{\sqrt{3}}{2}$. If the graph of $y = f(x)$ is shifted to the right by $\frac{π}{6}$ units and becomes symmetric about the $y$-axis, calculate the minimum value of $\omega$.

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