How do you manage enlarged pores when they are clogged with sebum?

Large pores are prominent on my nose and around it.

Blackheads are a problem, but sometimes sebum gets clogged in my pores, making my skin feel bumpy even after I apply makeup.

I try squeezing them out with my hands when washing my face, and I make an effort to keep my pores clean by removing sebum with cold showers or pore packs, but there is no way to stop the sebum from filling up once pores have widened.

How about others? Please share any special care tips you have.