If the function $f$ defined by
\[f(x) = \frac{cx}{2x + 3},\]where $c$ is a constant and $x \neq -\frac{3}{2},$ satisfies $f(f(x)) = x$ for all $x \neq -\frac{3}{2},$ then find $c.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If the function $f$ defined by
\[f(x) = \frac{cx}{2x + 3},\]where $c$ is a constant and $x \neq -\frac{3}{2},$ satisfies $f(f(x)) = x$ for all $x \neq -\frac{3}{2},$ then find $c.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-3
If the function $f$ defined by
\[f(x) = \frac{cx}{2x + 3},\]where $c$ is a constant and $x \neq -\frac{3}{2},$ satisfies $f(f(x)) = x$ for all $x \neq -\frac{3}{2},$ then find $c.$
train