如图平行四边形$ABCD$中,$AE$平分$\angle BAD$,交$CD$于点$E$.
$(1)$请用尺规作$\angle BCD$的角平分线$CF$,交$AB$于点$F(保留作图痕迹,不写作法)$；
$(2)$根据（1）的作图,证明:$AE$∥$CF.$请在答题卡上完成相应编号的填空.
证明:$\because$四边形$ABCD$是平行四边形,
$\therefore AB$∥$CD$,$\angle BAD=\angle BCD$,
$\therefore \angle ECF=$①______(两直线平行,内错角相等）,
又$\because AE$平分$\angle BAD$,$CF$平分$\angle BCD$,
$\therefore \angle EAF=$②______,$\angle ECF=$③______,
$\therefore \angle EAF=\angle ECF=\angle CFB$,
$\therefore AE$∥$CF$④______(填推理的依据).