
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 $$\overrightarrow {OA}=(\cos \frac {3}{2}x，\sin \frac {3}{2}x)$$, $$\overrightarrow {OB}=(\cos \frac {1}{2}x，-\sin \frac {1}{2}x)$$, and $$x∈[- \frac {π}{4}， \frac {π}{4}]$$.
(I) If $$f(x)= \overrightarrow {OA}\cdot \overrightarrow {OB}$$, find the analytical expression of function $f(x)$ with respect to $x$;
(II) Find the range of $f(x)$;
(III) Let $t=2f(x)+a$ have a range of $D$, and the function $$g(t)= \frac {1}{2}t^{2}+t-2$$ has a minimum value of 2 on $D$, find the value of $a$.

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