Learn Portuguese (Portugal): Eu queria que nós cooperássemos em harmonia.

The verb in the main clause, queria (wanted), is in a past tense. When you express a past desire, doubt, or emotion followed by que, the second verb must match that past timeline by using the imperfect subjunctive. If the sentence were in the present tense (I want us to cooperate), it would be Eu quero que nós cooperemos.

How exactly do we build the word cooperássemos?

For regular verbs, you start with the eles form of the simple past tense, which is cooperaram. Then, you drop the -ram ending to get your stem (coopera-) and add the imperfect subjunctive ending for nós, which is -ssemos. This gives us cooperássemos.

Why does cooperássemos have a written accent mark when the infinitive verb cooperar does not?

Adding the long -ssemos ending makes the word very long. To keep the spoken stress on the same vowel as the other imperfect subjunctive forms (like the eu form, cooperasse), a written accent is required on the nós form. For -ar verbs, this is always an acute accent, giving us the á in cooperássemos.

Could I just use the personal infinitive and say Eu queria nós cooperarmos?