
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 $f(x)=\cos \frac {x}{2}\sin \left( \frac {x}{2}+ \frac {\pi}{3}\right)- \sqrt {3}\cos ^{2} \frac {x}{2}+ \frac { \sqrt {3}}{4}$.  
(I) Find the intervals of monotonicity of $f(x)$ in the interval $[0,\pi]$.  
(II) If $f(x_{0})= \frac {2}{5}$, $x_{0}\in[0, \frac {\pi}{2}]$, find the value of $\sin x_{0}$.

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