1998 Accord cooling system question

1998 Accord LX , i4, auto, 65K miles

took it for an oil change, recommendation from the station: flush and change cooliing system due to it is being brown color.
Looked at the anteefreeze and it is brown, looks as if the fwole fluid was rusted, it does not looks like there is oil leak in the cooling system, but I may be wrong.
During oil change, they did not mention anything about anteefreeze leaking into oil.
Levels of oil or anteefreeze are steady all the time, no smoke from the pipes, no overheating, no warning lites.
This is an original anteefreeze and has never been changed or added to.
Should this be just anold fluid that is 9 years of age and it is time to service cooling system or I have some kind of problem on my hands?
My plan: flush and change cooling (will do it myself, does not looks that complicated according to Haynes) and see if it will solve it.

Any advise?

It is a good practice to flush your cooling system every 30,000 miles or every two years. So your are about 35,000 miles or 7 years late.

Do it asap and you may avoid more costly repairs down the road: clogged system, overheating, etc.

You are right: it is not very complicated, but considering lack of maintenance I recomend using chemicals to clean your system first.

Good luck,

Sam