Officially πηγαίνω is Present Tense and πάω is Future Tense.
So, all forms coming from the Present Tense (and therefore have continuous meaning ) use the stem of πηγαίνω.
Future Continuous -> θα πηγαίνω
Past Continuous -> πήγαινα
Future Continuous -> θα πηγαίνω
Subjunctive Continuous -> να πηγαίνω ( μου αρέσει να πηγαίνω βόλτα κάθε μέρα)
πάω is future tense, so its stem is used in all forms coming from the Future tense (and therefore with simple and not continuous meaning).
Simple Future ->θα πάω
Subjunct Simple -> να πάω (Θέλω να πάω βόλτα)
{Simple Past πήγα is irregular.}
In colloquial speach, however, we often use παω as Present tense (as a short form of πηγαίνω). Please pay special attention to this, as this is where most Greek language learners get confused.
Example:
Πού πας;
Πάω σχολείο. (πάω / πας are used instead of πηγαίνω / πηγαίνεις).
But in all other forms with continuous meaning we only use πηγαίνω. Πάω is wrong.
It is wrong if we say: “Μου αρέσει να πάω βόλτα κάθε μέρα.”
We must use the continuous form”πηγαίνω”: “Μου αρέσει να πηγαίνω βόλτα κάθε μέρα.”
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.