Value from an Iterated Integral Equation

Let $x$ and $y$ be functions of $t$ such that $x(0)=y(0)=1$. If $$x(t) = \int x(t)\ \mathrm{d}t + \iint x(t)\ \mathrm{d}t\ \mathrm{d}t + \iiint x(t)\ \mathrm{d}t\ \mathrm{d}t\ \mathrm{d}t + \dots $$ and $$y(t) = 2\left(\int y(t)\ \mathrm{d}t + \iint y(t)\ \mathrm{d}t\ \mathrm{d}t + \iiint y(t)\ \mathrm{d}t\ \mathrm{d}t\ \mathrm{d}t + \dots\right),$$ determine the value of $x(1)+y(1)$.