MN-MO 2001 Problem 1

Suppose that a sequence $x_1,x_2,\ldots,x_{2001}$ of positive real numbers satisfies $$3x^2_{n+1}=7x_nx_{n+1}-3x_{n+1}-2x^2_n+x_n\enspace\text{ and }\enspace x_{37}=x_{2001}.$$ Find the maximum possible value of $x_1$ .