
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 $f(x)=\sin (\omega x+\phi)$ $(\omega > 0,0 < \phi < \frac {\pi}{2})$, $f(x_{1})=1$, $f(x_{2})=0$, if $|x_{1}-x_{2}|_{min}= \frac {1}{2}$, and $f( \frac {1}{2})= \frac {1}{2}$, find the interval of monotonic increase for $f(x)$.

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