If $f(x) = |3x - 1|,$ compute all values of $x$ for which $f(f(x)) = x.$  Enter all the solutions, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $f(x) = |3x - 1|,$ compute all values of $x$ for which $f(f(x)) = x.$  Enter all the solutions, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{5}, \frac{1}{4}, \frac{2}{5}, \frac{1}{2}
If $f(x) = |3x - 1|,$ compute all values of $x$ for which $f(f(x)) = x.$  Enter all the solutions, separated by commas.
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