
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 $f(x)=\sin (2x- \frac {\pi}{6})$.  
(I) Find the smallest positive period of the function $f(x)$.  
(II) Find the interval of monotonic increase for the function $f(x)$.  
(III) When $x\in[0, \frac {2\pi}{3}]$, find the minimum value of the function $f(x)$, and find the corresponding $x$ value when $y=f(x)$ reaches its minimum value.

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