
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 $f(x)=\sin (\omega x+\varphi)$ with $\omega > 0$ and $|\varphi| < \frac {\pi}{2}$, the function has a minimum period of $4\pi$ and, after being shifted to the right by $\frac {2\pi}{3}$ units, becomes symmetric about the $y$-axis. Determine the value of $\varphi$.

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