
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 $|\varphi| < \frac {\pi}{2}$, calculate the value of $\varphi$ if the function has a minimum positive period of $\pi$ and its graph is translated to the right by $\frac {\pi}{6}$ units to obtain the graph of the function $g(x)=\sin \omega x$.

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