Hanoi Open Mathematics Competition 2013 Senior Question 11

Positive numbers \(a,b,c,d,p,q\) satisfy \((x+a)(x+b)(x+c)(x+d)=x^4+4px^3+6x^2+4qx+1\) for all real \(x\). Find the smallest value of \(p\) or the largest value of \(q\).