When regiments/LCTs/RCTs patrol, they typically do so along a length of border rather than one specific planet. Generally a component of the unit will remain on the nominal garrison world, while other task forces will head out to patrol or to garrison other nearby worlds, with the latter especially common with LCTs/RCTs. The patrolling will not only occur in the inhabited systems, but also the numerous unpopulated worlds that don't appear on the maps.
When patrolling inhabited systems, it's probably more a matter of showing the flag and resupply, as they will often be able to check in with then local planetary garrison and ask for a situation report. There may still be some need to do actual checks rather than just rely upon the word of the garrison, such as if the garrison only covers one continent on a world and lacks enough transport to be able to regularly check other garrisons.
With uninhabited systems, or those where the planetary garrison requires assistance, then the first step probably to just sweep the standard jump points, then go into orbit of any major worlds, especially those that could support life. Orbital surveys will probably be the main method of checking for signs of intruders, with follow ups by atmospheric flights and/or actual landings by a scout force, with the main force ready to drop if needed.
