The CMS experiment has greatly benefited from the utilization of the particle-flow (PF) algorithm for the offline reconstruction of data. The Phase II upgrade of the CMS detector for the High Luminosity upgrade of the LHC (HL-LHC) includes the introduction of both tracking and the new high-granularity calorimeters in the Level-1 trigger. The inclusion of tracking in particular offers the possibility of developing a simplified PF algorithm in the Level-1 trigger, as well as the possibility for the use of advanced pileup (PU) mitigation techniques such as Pileup Per Particle Identification (PUPPI). We present the logic of these algorithms, along with their inputs and possible implementation using prototype hardware. We show that these implementations are capable of operating within the budgeted latency requirements of the Level-1 trigger environment. The expected performance and physics implications of such algorithms are shown using Monte Carlo samples with 200 pileup, simulating the harsh conditions of the HL-LHC. We discuss the importance of these advanced techniques in preserving the physics performance in the high-intensity environment.