Singular or plural

Which is correct:

Our 'brains/brain' 'is/are' very complex?

Our 'brains/brain' 'control/controls' everything

Also:

There 'is or are' many resasons why we should take care of our brains/brain.

Please help me with this problem. Can I mix singular with plural here or what? Can each sentence be written in both singular and plural form? Is there a rule that would help me out?

Thank you.