
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 $$\overrightarrow {a} = (\cos \frac {3θ}{2}, \sin \frac {3θ}{2})$$, $$\overrightarrow {b} = (\cos \frac {θ}{2}, -\sin \frac {θ}{2})$$, and $$θ∈[0, \frac {π}{3}]$$  
(I) Find the maximum and minimum values of $$\frac { \overrightarrow {a}\cdot \overrightarrow {b}}{| \overrightarrow {a}+ \overrightarrow {b}|}$$;  
(II) Determine if there exists a value of k such that $$|k \overrightarrow {a}+ \overrightarrow {b}|= \sqrt {3}| \overrightarrow {a}-k \overrightarrow {b}|$$?

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