Help with IF AND formula - beginner/intermediate user

Hello,

This is my first post, and I am having problems with a IF AND formula. To give a little background, I use excel in a construction engineering capacity, which is often using excel for quantity takeoffs and cost estimation. Occasionally I do a lookup table or more advanced formula. I feel my skills haven't gotten beyond beginner/intermediate level. That being said, here is my problem.

I have used excel to create a spreadsheet for evaluating fire escape components and created a table (albiet not the best way) to score them across various sheets. That part works fine. I've taken these component scores, created an overall average, and a specific component average (tread and landing), and summarized that in another sheet. Also works fine.

Now here is where i have a problem. I am trying to create a formula that automatically prioritizes these scores.

Average Overall Score </=60 + Tread and Landing Score <10 Priority 1
Average Overall Score >60 but </=65 and Tread and Landing Score <15 Priority 2
Average Overall Score >65 and Tread and Landing Score <20 Priority 3

My formula is this =IF(AND(OR(F3=60,F3<60),G3<6),1,IF(AND(OR(60<F3,60=F3),OR(F3<70,F3=65),G3<13),2,3))
where F3 is the overall score, and G3 is the tread and landing score

When I looked at the results I had one cell with an overall score of 68.5 and a tread and landing score of 14 and it gave me a priority of 2. I would have thought it should have given me a 3 (See Summary sheet row 28) It made me wonder if my formula was correct. If I have to check everything line by line it sort of defeats my purpose.

I am looking at the way I scored things to see if it makes sense or need to make adjustments. Hopefully I can just change a value here or there to correct the problem. Ive attached the spread sheet (created in 2007 but Im working in 2003) if anyone can advise me if my formula is correct. I noticed the problem in the summary sheet row H.

Thanks for any help you can provide.