An ordered triple of pairwise distinct real numbers \((a,b,c)\) is called **tripping** if it satisfies \[
\begin{cases}
3a+b=a^3,\\
3b+c=b^3,\\
3c+a=c^3.\\
\end{cases}
\]

How many tripping triples are there?

**Details and assumptions**

A set of values is called **pairwise distinct** if no two of them are equal. For example, the set \( \{1, 2, 2\} \) is not pairwise distinct, because the last 2 values are the same.

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