1. The rule.
So + "verb" + I is used if you want to say that a positive statement is also true for you.
Neither + "verb" + I is used if you want to say that a negative statement is also true for you.
2. How to write the verb correctly?
If we have "am / is / are (not)" in the statement, we use "am" in the reply.
If we have "have / has (not)" (for possessions) in the statement, we use "have" in the reply.
If we have "can(not)" in the statement, we use "can" in the reply.
If we have other verbs - (don't / doesn't go), do, like, play, etc. and have (for actions) - in the statement, we use "do" in the reply.
3. Some examples with different verbs.
"do"
Ellen: I like playing the guitar.
I: So do I.
Ron: I don't wake up early at the weekend.
I: Neither do I.
"am"
Alice: I am a student.
I: So am I.
Martin: I am not a doctor.
I: Neither am I.
"can"
Molly: She can speak Spanish.
I: So can I.
Nick: I can't speak Chinese.
I: Neither can I.
"have" (possession)
Amelie: We have got a cat.
I: So have I.
Frank: My friend hasn't got a car.
I: Neither have I.
Зверни увагу!
Note!
If we speak about actions we cannot use "have" in the reply. We should use "do".
"have" (action)
Sonia: I have my yoga class twice a week.
I: So do I.
Tom: My brother doesn't have coffee for breakfast.
I: Neither do I.