"do you think I should...?" Questions

Hi,

I have some issues with an exercise I have to do.

I have to complete the questions with do you think I should …? and an idea form the box (there is a box and several words in it).

I will write down two of the sentences:

Everything on the menu looks wonderful!
What do you think I should have?

My aunt has invited me to her picnic, but I don’t want to go?
What do you think I should say to her?

In italic are my answers, but according to the answers of my workbook (New Headway, Intermediate, Fourth Edition) they are not correct. The correct answers, written on the back of the workbook, are:

Everything on the menu looks wonderful!
What do you think I should I have?

My aunt has invited me to her picnic, but I don’t want to go?
What do you think I should I say to her?

Would you somebody explain to me why do we need “I” after “should” in such cases?

Thanks in advanced!

P.S. Please, excuse my English, if it doesn’t sound pretty right, but I’m learning it : )