Any rule for verb form after "...to come and speak to us"
I was working through gerunds and infinitives with a class and the following gap fill sentence was given; (gaps were (give) (come) (talk)):
"We really do appreciate your giving (give) up your valuable time to come (come) and talk (talk) to us".
I can see rules in the book's gerunds and infinitives grammar sections that indicate a gerund follows the verb "appreciate" hence ..."appreciate your giving up..."
and that the infinitive with to is used to expresses purpose hence "...to come..", but is there are rule to say why "speak" must be a bare infinitive (without "to")?
Is it something to do with a verb following the conjunction "AND"?