
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 $\overrightarrow{a}=(\cos \frac {3}{2}x,\sin \frac {3}{2}x)$, $\overrightarrow{b}=(\cos \frac {1}{2}x,-\sin \frac {1}{2}x)$, and $x\in[0, \frac {\pi}{2}]$
(I) Find $\overrightarrow{a}\cdot \overrightarrow{b}$ and $|\overrightarrow{a}+ \overrightarrow{b}|$;
(II) If the minimum value of the function $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}-4m|\overrightarrow{a}+ \overrightarrow{b}|+1$ is $(-\frac {1}{2})$, find the value of $m$.

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