nouns - The use of reflexive pronouns

I am currently doing homework for a linguistics course I am taking.

The question is about creating a rule to make confirm if certain sentences are grammatical or ungrammatical.

Here are some examples, with those with a star in front signifying that the sentence is ungrammatical.

Set 1:

a. I saw myself in the mirror.

b. * Myself saw me in the mirror.

c. I showed the monkey himself in the mirror.

d. * I showed himself the monkey in the mirror.

Set 2:

a. Carla read a book about herself.

b. * A book about Carla upset herself.

c. John’s teachers respect themselves.

d. * John’s teachers respect himself.

Set 3:

a. I know that Mary likes herself.

b. * I know that Mary likes myself.

For this homework, I need to create a rule to make all those sentences with no * grammatical, and all the sentences with * ungrammatical. This rule has to apply for all 3 sets of sentences.

Currently, the rule I have come up with is:
A reflexive pronoun can only be used to an entity that has already been mentioned.

However, this rule only can be applied to sets 1 and 2.

Does anyone have any idea on a rule that can be applied to all 3 sets?