By action do you mean turns/moves? I’m not really sure about a second action in the Pokédex, but there is a way to ensure you won’t lose your catch combo.
If the first pokeball you throw does not catch the Pokémon, run away from it. Pokémon cannot run away from you before you throw a pokeball, so to be safe I always run away if the first pokeball I throw doesn’t work (since running doesn’t affect the chain) Also, the only ways you can break the chain are if:
1) You defeat the Pokémon
2) The Pokémon runs away from you
3) You close your game (close the software)
4) Catch another species of Pokémon
I hope this answer helped you! Good luck on catching your shiny Caterpie! :)