I saw your question as a interesting one at first, but i think now it has a simple answer. Firstly i would answer your second example:---emruz vaght nadaram. farda miayam. What do you say this sentence in English? " I am busy today, and i will go to your home tommorow" OR "I am busy today, and i will come to your home tommorow" ? I think the second one is correct. It means you should use of " Come" in your sentence. " i will come to your home tommorow". So i would clarify that "Go" means "raftan" and "Come" mean "amadan" in Persian. But in first sentence, " ... shoma ba ma miayid?" ... I think in this case "miayid" means " Hamrahi kardan", Or " walking together to the park! ". Hope to get your answer, But you can ask more details, if it is not clear yet.

1. In 'shomā bā mā miāyid', the verb 'آمَدَن' actually means 'to accompany + to arrive there'. Amazingly, saying 'shomā bā mā miravid' is almost senseless in this dialogue. Therefore, when inviting someone to come to a place with you, use 'آمَدَن' or ‘to come’. 2. Again, it's the 'one-on-one' dialogue that makes the conversation suitable for the verb 'آمَدَن' and not 'رَفتَن' (‘to go’). If she asked her whether she wanted to go to someone else's home, then you would use 'رَفتَن'. To make it clear, let's consider these examples: *Why don't you come to our house? *I’ll come to your house soon. چِرا بِه خانه‌یِ ما نمی‌آیی؟ Cherā be khāneye mā nemiāyee? بِه زودی بِه خانه‌یِ شُما می‌آیَم. Be zudi be khāneye shomā miāyam. ---------------------- *Why don’t you go to her house? *I’ll go see her soon. چِرا بِه خانه‌یِ او نمی‌رَوی؟ Cherā be khāneye oo nemiravi? بِه زودی می‌رَوَم و او را می‌بینَم. Be zudi miravam va oo rā mibinam.