Obligatory Six Afraid of Seven Joke

The positive integers \(x_{1}\ldots,x_{7}\) satisfy the condition \( x_{6}=144\) and \[ x_{n+3}=x_{n+2}(x_{n+1}+x_{n})\] where \( n = 1,2,3,4\) Then what is the value of \(x_{7}\)


Source: Poland Mathematical Olympiad in 1997.
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