
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 $f(x)=\sin (\omega x+\varphi)$ $(\omega > 0,0 < \varphi < \pi)$ has a minimum positive period of $\pi$, and its graph is symmetric about the line $x= \frac {\pi}{6}$.  
$(1)$ Find the values of $\omega$ and $\varphi$;  
$(2)$ If $f( \frac {\alpha}{2}- \frac {\pi}{12})= \frac {3}{5}$, where $\alpha$ is an acute angle, find the value of $\cos (\alpha- \frac {\pi}{3})$.

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