I would like to know where is the brake,

That is strange because they are unrelated.

The power steering works using a pump that has a pulley and is turned by the Serpentine belt. Where you put the fluid, did it look like this?

https://www.carparts.com/power-steering-pump/jeep/grand-cherokee/2003

https://www.google.com/search?q=2003+jeep+grand+cherokee+power+steering+pump

The Brake Master Cylinder has a similar reservoir and also has a brake booster that uses vacuum power from the engine to give you a mechanical advantage. Both are shown here

https://www.ebay.com/b/Brake-Master-Cylinders-Parts-for-Jeep-Grand-Cherokee-for-2003/33566/bn_87327012

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Your 97 Jeep Grand Cherokee takes ATF+4 any other fluid type will damage your transmission

foaming transmission oil is normally from incorrect oil level in transmission
check the level -hot, running and in drive
ensure somebody has their foot on the brake while carrying out the check

the valve body may be the issue in transmission

NO!!!

it is probably not gearbox oil. it is probably transmission fluid because it travels through the radiator cooling tanks. the cooling tanks may have a leak causeing the fluids to leak into the radiator.

Although this may be due to a transmission trying to fail, it is more likely to be a problem with the transmission cooler or connection hoses. You will have to inspect them from underneath the vehicle. Check the fluid level to see if it has lost fluid too but follow the instructions in the owner's manual as there is a specified procedure for checking this and ignoring it will lead to a false reading.

Get a funnel and add it to where you pulled the dipstick out of to check it.If you dont know where the dipstick is check by where you add the brake fluid it should be right off to the left but down toward the engine more

What fluid are you tryin to put in?

sounds like a faulty transmission bud.

Could be low fluid, burnt fluid, or worn one-way clutch or brakebands.

Best to let an autobox specialist try it out and give you a full opinion.