
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 planar vector $\overrightarrow {a}$=（cosx，sinx）, $\overrightarrow {b}$=（ $\frac { \sqrt {2}}{2}$， $\frac { \sqrt {2}}{2}$）, and $|$ $\overrightarrow {a}$-$ \overrightarrow {b}$$|$= $\frac {4 \sqrt {5}}{5}$．
(Ⅰ) Find the value of cos（x-$ \frac {π}{4}$）;
(Ⅱ) If x∈[ $ \frac {π}{2}$， $ \frac {3π}{2}$], find the value of cos2x.

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