
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 $f(x)=\sin (\omega x- \frac {\pi}{6})+ \frac {1}{2}(\omega > 0)$, and $f(a)=- \frac {1}{2}$, $f(\beta)= \frac {1}{2}$. If the minimum value of $|α-β|$ is $\frac {3\pi}{4}$, determine the interval of monotonic increase for the function.

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