
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 $\overrightarrow {a}=( \sqrt {3}\sin2x，\cos2x)$, $\overrightarrow {b}=(\cos2x，-\cos2x)$  
(I) If $x\in( \frac {7\pi}{24}， \frac {5\pi}{12})$ and $\overrightarrow {a}\cdot \overrightarrow {b}+ \frac {1}{2}=- \frac {3}{5}$, find $\cos4x$;  
(II) If $x\in(0， \frac {\pi}{3}]$ and the equation about $x$, $\overrightarrow {a}\cdot \overrightarrow {b}+ \frac {1}{2}=m$, has exactly one real root, find the value of $m$.

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