It has a weak determiner so it has to have a strong adjective.
Whenever you have a noun phrase, you generally have a determiner at the front, then a chain of adjectives, and finally a noun at the end. "The big bad wolf" has a determiner "the" two adjectives, and a noun. Determiners in English include words like the, a, one, two, some, many, etc.
In German, a determiner is strong if it has endings like der does. It is weak if it doesn't have an ending. It's also weak if it isn't there at all. (Typically with plurals.)
A strong adjective takes pretty much the same endings as der does. A weak adjective only takes -e or -en, depending on the number, case, and gender.
I have a system to memorize the different case endings, if you want to look at it. Everyone seems to have their own take on the best way to learn them, but this is what works for me.
You have another useful link for the ending of adjective
This is not a phonetic thing but a morphosyntatic matter. http://en.wiktionary.org/wiki/gro%C3%9F#Declension
"großes" is used for neuter words that are the direct object of the sentence, and have an indefinite article. These pages may help with adjective endings:
This is very useful site in helping your understanding of the use of Alle and how it differs to Jedes. Hope it helps :-)
"das große Fenster" but "ein großes Fenster" https://en.wiktionary.org/wiki/gro%C3%9F#Declension