
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
Let the function $f(x) = \frac{2x-3}{2x+1} + a$ have its range as set $A$ over the interval $\left[0, \frac{3}{2}\right]$, and let the function $g(x) = \sqrt{x+2} + \sqrt{2-x}$ have its domain as set $B$.  
(1) If $a=0$, find the complement of $A \cap B$ in $\mathbb{R}$.  
(2) If $A \cap B = A$, find the range of the real number $a$.

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