
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 $f(x)=2\sin (x- \frac {π}{6})\sin (x+ \frac {π}{3})$, $x\in R$.
(I) Find the smallest positive period of the function $f(x)$;
(II) In $\triangle ABC$, if $A= \frac {π}{4}$, and acute angle $C$ satisfies $f( \frac {C}{2}+ \frac {π}{6})= \frac {1}{2}$, find the value of $\frac {BC}{AB}$.

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