SmileBASIC, 241 bytes

INPUT N
T=N*2CLS?" "*N;"__"*N
DIM B[T]FOR I=-1TO N-1O=1P=N+I*2FOR J=0TO T-1IF I<0THEN O=ABS(J0N+.5)<<0B[J]=O?" "*O;MID$("\/\",J<N,2)*(T-O)ELSE R=P<N*3+I*2-J&&RND(2)P=P+(R*2-1)*(O==R)A=P<=B[J]R=R||A:P=P+A:LOCATE P,J+1?"_"B[J]=P+1O=R
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Heavily based off of Matty's answer