
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 vectors $\overrightarrow{a}=(2\sin (x+ \frac {\pi}{6}),-2)$, $\overrightarrow{b}=(2, \frac { \sqrt {3}}{2}-2\cos x)$.  
(Ⅰ) If $\overrightarrow{a}\perp \overrightarrow{b}$, find the value of $\sin (x+ \frac {4\pi}{3})$;  
(Ⅱ) Let $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}$, if $x\in[0,\pi]$, find the range of $f(x)$.

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