If $f(x)=\dfrac{a}{x+2}$, solve for the value of $a$ so that $f(0)=f^{-1}(3a)$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $f(x)=\dfrac{a}{x+2}$, solve for the value of $a$ so that $f(0)=f^{-1}(3a)$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-\frac{10}{3}
If $f(x)=\dfrac{a}{x+2}$, solve for the value of $a$ so that $f(0)=f^{-1}(3a)$.
train