
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 function $f(x)=\frac{2x-3}{2x+1}+a$ defined on the interval $[0,\frac{3}{2}]$ with a range of set $A$, and the function $g(x)=\sqrt{x+2}+\sqrt{2-x}$ with a domain of set $B$.

(1) If $a=0$, find the complement of $A∩B$.

(2) If $A∩B=A$, find the range of real number $a$.

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