Public Economics Social Security Question

Just looking for some insight on a prompt for a midterm...

Suppose you are advising a family friend who is currently working at age 66 and who is considering whether to work an additional year, or whether to fully retire and begin collecting Social Security. Explain to her the advantages and disadvantages (in principle) of working one more year. Finally, suppose she confides that her doctor has told her that she has a 50% chance of dying within the next 5 years. From a purely financial standpoint, explain whether it would be better to work an additional year, or to retire now.

I'm answering this assuming she was born post 1960, w/ the FBA being 67. What I've got for the advantages

• Additional year of pay
• Possibility to raise her 35 year earning average (AIME)
• Won't get the 6.67% less in PIA for collecting SS a year early

Disadvantages

• Tax on the earnings of the final year

Can't think of any others, but for the second part of the question, I can't figure how to come to a financial conclusion of whether to work an additional year provided she has a 50% chance of 5 years left. Can anybody explain their logic?

Thanks!