AOC and 529 coordination of QEE and taxable scholarships.

My daughter is in college and I am trying to determine what I can take out of her 529 plan:

Scholarship: 2500 School grant: 4000 Pell: 5500 Total scholarships: 12000

Tuition, fees, books: 8000

Room and Board: 11000

The options I am considering:

1) Taxable scholarship amount is 4000. 529 QEE: 11000 AOC QEE=0 2) Declaring additional 2000 as taxable on my daughter's return. Taxable scholarship amount is 6000. 529 QEE: 11000 AOC QEE 00

Do I understand Pub 870 correctly that the 529 QEE is NOT reduced by the taxable amount of her scholarship. So declaring an additional

2000 as taxable income has no impact on the expenses claimed for the 529 distribution nor does the original require 4000 taxable amount.

Note: The scholarship and school grant can be used for any expense included in the COA. It is not restricted.