Samkhya's model of a single episode of embodied experience is sequential, and pani's place in that sequence is near the very end of it. An organ of perception, say chakshu, makes contact with rupa; manas synthesises the resulting data into a presented object; ahamkara claims the experience as belonging to a self; buddhi renders a judgment about what to do; and only then, if the judgment calls for grasping something, does pani act. Every stage before pani's is either receptive or coordinating or evaluative; pani is where the sequence finally produces an effect on the external world.
This ordering is part of why Samkhya can maintain that perception and action are structurally distinct kinds of tattva-activity even though, in lived experience, they are constantly interleaved, reaching for an object typically happens while still looking at it, with vision and grasping operating together rather than in the strict serial order the philosophical analysis lays out. The classical texts are describing the metaphysical dependency between the stages, what presupposes what, rather than claiming that a person actually pauses at each stage before proceeding to the next.
Pani, alongside vak, pada, payu and upastha, completes the set of five Karmendriyas, and together with manas and the five Jnanendriyas forms the eleven organs Samkhya treats as the complete instrumental apparatus standing between an unconscious material world and the appearance, produced by proximity to purusha, of a self experiencing and acting within it.