我觉得你的解释很好！感觉比原来的解释更有说服力。古文功底好啊！

任，control, manage,drive, means choose appropriate person to control or manage the power of situations.

li, interest, zhi, control, manipulate, so "take the advantage of circumstances is to manipulate the power of situations according to the interests, which different parties try to persuing." That means, take advantage of circumstances means, how to attract others with interests they are seeking and try to manipulate their seeking of interest to a invisible power of my control against them.