What is the difference between rely on and trust me?

[Rag Ram]

Business Idiom in English, Intermediate level

ESL/EFL Test #131 "Ways of approving", question 7

You can ......... on me to support you when the matter is discussed at the next meeting.

(a) rely
(b) trust
(c) believe
(d) follow

Business Idiom in English, Intermediate level

ESL/EFL Test #131 "Ways of approving", answer 7

You can rely on me to support you when the matter is discussed at the next meeting.

Correct answer: (a) rely

Your answer was: incorrect
You can trust on me to support you when the matter is discussed at the next meeting.
_________________________

why don't we use trust me. instead of rely ?

[Conchita]

We could say 'trust me', but not 'trust on me'.