Question 1200315
<br>
Here is a diagram with critical points labeled:<br>
{{{drawing(500,400,-10,10,-8,8
,line(-8,0,8,0)
,circle(0,0,2),circle(0,0,4),circle(0,0,6)
,locate(-8,.75,A),locate(-5.75,.75,B),locate(-3.75,.75,C),locate(-1.75,.75,D)
,locate(2.25,.75,E),locate(4.25,.75,F),locate(6.25,.75,G),locate(8,.75,H)
,locate(0,6.75,I),locate(0,4.75,J),locate(0,2.75,K),locate(0,-1.25,L),locate(0,-3.25,M),locate(0,-5.25,N)
)}}}<br>
One path that satisfies the requirements is this:<br>
A B I G F J C D K E D L E F M C B N G H<br>