Multi field search

Hi,
I need to build a search for my wordpress site.
the search should contain two fields:

1.input field that takes a category name from user
2. taxonomy dropdown

the user for example prints “cars” in the input field and selects USA option from the taxonomy dropdown and the results page should display all of my custom posts assigned to cars category and to USA term.

i don’t want to display my categories in dropdown as i have > 1000 category.

I can’t figure how to do that!
any help would be appreciated!