VMO 2005 Problem 6

Let $\{x_n\}$ be a real sequence defined by: $$x_1=a,x_{n+1}=3x_n^3-7x_n^2+5x_n$$ For all $n=1,2,3...$ and a is a real number. Find all $a$ such that $\{x_n\}$ has finite limit when $n\to +\infty$ and find the finite limit in that cases.