
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 $f(x)=A\sin (\omega x+\varphi)$ ($A > 0$, $\omega > 0$, $0 < \varphi < \pi$) reaches its maximum value of $4$ at $x= \frac {\pi}{12}$, and within the same period, it reaches its minimum value of $-4$ at $x= \frac {5\pi}{12}$.  
$(1)$ Find the intervals of monotonic increase for the function $f(x)$ on $[0, \frac {2\pi}{3}]$;  
$(2)$ If $f( \frac {2}{3}\alpha+ \frac {\pi}{12})=2$, $\alpha\in(0,\pi)$, find the value of $\alpha$.

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